{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T16:25:40Z","timestamp":1777479940969,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s10485-019-09556-y","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T13:53:10Z","timestamp":1547646790000},"page":"323-363","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hom\u2013Tensor Categories and the Hom\u2013Yang\u2013Baxter Equation"],"prefix":"10.1007","volume":"27","author":[{"given":"Florin","family":"Panaite","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul T.","family":"Schrader","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8554-4466","authenticated-orcid":false,"given":"Mihai D.","family":"Staic","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"9556_CR1","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/0370-2693(91)90671-C","volume":"256","author":"N Aizawa","year":"1991","unstructured":"Aizawa, N., Sato, H.: $$q$$ q -deformation of the Virasoro algebra with central extension. Phys. Lett. B 256, 185\u2013190 (1991)","journal-title":"Phys. Lett. B"},{"key":"9556_CR2","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/0003-4916(72)90335-1","volume":"70","author":"RJ Baxter","year":"1972","unstructured":"Baxter, R.J.: Partition function of the eight-vertex lattice model. Ann. Phys. 70, 193\u2013228 (1972)","journal-title":"Ann. Phys."},{"key":"9556_CR3","first-page":"1887","volume":"256","author":"J B\u00e9nabou","year":"1963","unstructured":"B\u00e9nabou, J.: Cat\u00e9gories avec multiplication. C. R. Acad. Sci. Paris Ser. I Math. 256, 1887\u20131890 (1963)","journal-title":"C. R. Acad. Sci. Paris Ser. I Math."},{"key":"9556_CR4","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.geomphys.2013.10.010","volume":"76","author":"S Benayadi","year":"2014","unstructured":"Benayadi, S., Makhlouf, A.: Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. J. Geom. Phys. 76, 38\u201360 (2014)","journal-title":"J. Geom. Phys."},{"key":"9556_CR5","doi-asserted-by":"publisher","first-page":"2216","DOI":"10.1080\/00927872.2010.490800","volume":"39","author":"S Caenepeel","year":"2011","unstructured":"Caenepeel, S., Goyvaerts, I.: Monoidal Hom-Hopf algebras. Commun. Algebra 39, 2216\u20132240 (2011)","journal-title":"Commun. Algebra"},{"key":"9556_CR6","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1016\/0370-2693(90)91196-I","volume":"237","author":"M Chaichian","year":"1990","unstructured":"Chaichian, M., Kulish, P., Lukierski, J.: $$q$$ q -deformed Jacobi identity, $$q$$ q -oscillators and $$q$$ q -deformed infinite-dimensional algebras. Phys. Lett. B 237, 401\u2013406 (1990)","journal-title":"Phys. Lett. B"},{"key":"9556_CR7","doi-asserted-by":"publisher","first-page":"073515","DOI":"10.1063\/1.4813447","volume":"54","author":"Y Chen","year":"2013","unstructured":"Chen, Y., Wang, Z., Zhang, L.: Integrals for monoidal Hom-Hopf algebras and their applications. J. Math. Phys. 54, 073515 (2013)","journal-title":"J. Math. Phys."},{"key":"9556_CR8","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0370-2693(90)90845-W","volume":"243","author":"TL Curtright","year":"1990","unstructured":"Curtright, T.L., Zachos, C.K.: Deforming maps for quantum algebras. Phys. Lett. B 243, 237\u2013244 (1990)","journal-title":"Phys. Lett. B"},{"key":"9556_CR9","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1142\/S0217732392000793","volume":"7","author":"C Daskaloyannis","year":"1992","unstructured":"Daskaloyannis, C.: Generalized deformed Virasoro algebras. Modern Phys. Lett. A 7, 809\u2013816 (1992)","journal-title":"Modern Phys. Lett. A"},{"key":"9556_CR10","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s11464-016-0544-9","volume":"11","author":"L Guo","year":"2016","unstructured":"Guo, L., Zheng, S.: Free involutive Hom-semigroups and Hom-associative algebras. Front. Math. China 11, 497\u2013508 (2016)","journal-title":"Front. Math. China"},{"key":"9556_CR11","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1016\/j.jalgebra.2005.07.036","volume":"295","author":"JT Hartwig","year":"2006","unstructured":"Hartwig, J.T., Larsson, D., Silvestrov, S.: Deformations of Lie algebras using $$\\sigma $$ \u03c3 -derivations. J. Algebra 295, 314\u2013361 (2006)","journal-title":"J. Algebra"},{"key":"9556_CR12","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.geomphys.2015.07.026","volume":"98","author":"M Hassanzadeh","year":"2015","unstructured":"Hassanzadeh, M., Shapiro, I., S\u00fctl\u00fc, S.: Cyclic homology for Hom-associative algebras. J. Geom. Phys. 98, 40\u201356 (2015)","journal-title":"J. Geom. Phys."},{"key":"9556_CR13","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1006\/aima.1993.1055","volume":"102","author":"A Joyal","year":"1993","unstructured":"Joyal, A., Street, R.: Braided tensor categories. Adv. Math. 102, 20\u201378 (1993)","journal-title":"Adv. Math."},{"key":"9556_CR14","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/BF02102632","volume":"146","author":"C Kassel","year":"1992","unstructured":"Kassel, C.: Cyclic homology of differential operators, the Virasoro algebra and a $$q$$ q -analogue. Commun. Math. Phys. 146, 343\u2013356 (1992)","journal-title":"Commun. Math. Phys."},{"key":"9556_CR15","volume-title":"Quantum Groups, Graduate Texts in Mathematics 155","author":"C Kassel","year":"1995","unstructured":"Kassel, C.: Quantum Groups, Graduate Texts in Mathematics 155. Springer, New York (1995)"},{"key":"9556_CR16","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.jalgebra.2005.02.032","volume":"288","author":"D Larsson","year":"2005","unstructured":"Larsson, D., Silvestrov, S.: Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities. J. Algebra 288, 321\u2013344 (2005)","journal-title":"J. Algebra"},{"key":"9556_CR17","doi-asserted-by":"publisher","first-page":"031701","DOI":"10.1063\/1.4866760","volume":"55","author":"L Liu","year":"2016","unstructured":"Liu, L., Shen, B.: Radford\u2019s biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras. J. Math. Phys. 55, 031701 (2016)","journal-title":"J. Math. Phys."},{"key":"9556_CR18","doi-asserted-by":"publisher","first-page":"013501","DOI":"10.1063\/1.4858875","volume":"55","author":"A Makhlouf","year":"2014","unstructured":"Makhlouf, A., Panaite, F.: Yetter-Drinfeld modules for Hom-bialgebras. J. Math. Phys. 55, 013501 (2014)","journal-title":"J. Math. Phys."},{"key":"9556_CR19","doi-asserted-by":"publisher","first-page":"51","DOI":"10.4303\/jglta\/S070206","volume":"2","author":"A Makhlouf","year":"2008","unstructured":"Makhlouf, A., Silvestrov, S.: Hom-algebra structures. J. Gen. Lie Theory Appl. 2, 51\u201364 (2008)","journal-title":"J. Gen. Lie Theory Appl."},{"key":"9556_CR20","first-page":"189","volume-title":"Generalized Lie theory in Mathematics, Physics and Beyond","author":"A Makhlouf","year":"2008","unstructured":"Makhlouf, A., Silvestrov, S.: Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras. In: Silvestrov, S., Paal, E., Abramov, V., Stolin, A. (eds.) Generalized Lie theory in Mathematics, Physics and Beyond, pp. 189\u2013206. Springer, Berlin (2008)"},{"key":"9556_CR21","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1142\/S0219498810004117","volume":"9","author":"A Makhlouf","year":"2010","unstructured":"Makhlouf, A., Silvestrov, S.: Hom-algebras and Hom-coalgebras. J. Algebra Appl. 9, 553\u2013589 (2010)","journal-title":"J. Algebra Appl."},{"key":"9556_CR22","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1007\/s10468-011-9280-8","volume":"6","author":"Y Sheng","year":"2012","unstructured":"Sheng, Y.: Representations of Hom-Lie algebras. Algebr. Represent. Theory 6, 1081\u20131098 (2012)","journal-title":"Algebr. Represent. Theory"},{"key":"9556_CR23","series-title":"De Gruyter Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1515\/9783110883275","volume-title":"Quantum Invariants of Knots and 3-Manifolds","author":"VG Turaev","year":"1994","unstructured":"Turaev, V.G.: Quantum Invariants of Knots and 3-Manifolds. De Gruyter Studies in Mathematics, vol. 18. Walter de Gruyter, Berlin (1994)"},{"key":"9556_CR24","doi-asserted-by":"publisher","first-page":"1312","DOI":"10.1103\/PhysRevLett.19.1312","volume":"19","author":"CN Yang","year":"1967","unstructured":"Yang, C.N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Phys. Rev. Lett. 19, 1312\u20131315 (1967)","journal-title":"Phys. Rev. Lett."},{"key":"9556_CR25","unstructured":"Yau, D.: Module Hom-algebras (2008). arXiv:0812.4695"},{"key":"9556_CR26","doi-asserted-by":"publisher","first-page":"165202","DOI":"10.1088\/1751-8113\/42\/16\/165202","volume":"42","author":"D Yau","year":"2009","unstructured":"Yau, D.: The Hom\u2013Yang\u2013Baxter equation, Hom\u2013Lie algebras, and quasi-triangular bialgebras. J. Phys. A Math. Theor. 42, 165202 (2009)","journal-title":"J. Phys. A Math. Theor."},{"key":"9556_CR27","unstructured":"Yau, D.: Hom-quantum groups III: representations and module Hom-algebras (2009). arXiv:0911.5402"},{"key":"9556_CR28","first-page":"45","volume":"8","author":"D Yau","year":"2010","unstructured":"Yau, D.: Hom-bialgebras and comodule Hom-algebras. Int. Electron. J. Algebra 8, 45\u201364 (2010)","journal-title":"Int. Electron. J. Algebra"},{"key":"9556_CR29","doi-asserted-by":"publisher","first-page":"065203","DOI":"10.1088\/1751-8113\/45\/6\/065203","volume":"45","author":"D Yau","year":"2012","unstructured":"Yau, D.: Hom-quantum groups I: quasi-triangular Hom-bialgebras. J. Phys. A Math. Theor. 45, 065203 (2012)","journal-title":"J. Phys. A Math. Theor."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10485-019-09556-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-019-09556-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-019-09556-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,22]],"date-time":"2020-11-22T17:32:01Z","timestamp":1606066321000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10485-019-09556-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["9556"],"URL":"https:\/\/doi.org\/10.1007\/s10485-019-09556-y","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"value":"0927-2852","type":"print"},{"value":"1572-9095","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,16]]},"assertion":[{"value":"28 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}