{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:41:14Z","timestamp":1760150474522,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T00:00:00Z","timestamp":1701993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501274","LJKMZ20220454","LJKZ0096"],"award-info":[{"award-number":["11501274","LJKMZ20220454","LJKZ0096"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Educational Department of Liaoning Province, China","award":["11501274","LJKMZ20220454","LJKZ0096"],"award-info":[{"award-number":["11501274","LJKMZ20220454","LJKZ0096"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Over a field of characteristic p&gt;3, let KO(n,n+1;t\u0332) denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra KO(n,n+1;t\u0332) are studied. Let TKO be a torus of KO(n,n+1;t\u0332), which is an abelian subalgebra of KO(n,n+1;t\u0332). By applying the weight space decomposition approach of KO(n,n+1;t\u0332) with respect to TKO, we show that all skew-symmetric super-biderivations of KO(n,n+1;t\u0332) are inner super-biderivations.<\/jats:p>","DOI":"10.3390\/axioms12121108","type":"journal-article","created":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T05:47:30Z","timestamp":1702014450000},"page":"1108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Note on Finite Dimensional Odd Contact Lie Superalgebra in Prime Characteristic"],"prefix":"10.3390","volume":"12","author":[{"given":"Xiaoning","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]},{"given":"Qiyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/0001-8708(77)90017-2","article-title":"Lie superalgebras","volume":"26","author":"Kac","year":"1977","journal-title":"Adv. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/aima.1998.1756","article-title":"Classification of infinite-dimensional simple linearly compact Lie superalgebras","volume":"139","author":"Kac","year":"1998","journal-title":"Adv. Math."},{"key":"ref_3","first-page":"81","article-title":"A survey of Lie superalgebras","volume":"1","author":"Sun","year":"1983","journal-title":"Adv. Phys. (PRC)"},{"key":"ref_4","unstructured":"Sun, H.Z., and Han, Q.Z. (1999). Lie Algebras, Lie Superalgebras and Their Applications in Physics, Peking Univ. Press. (In Chinese)."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Scheunert, M. (1979). Theory of Lie Superalgebras, Springer. Lecture Notes in Math.","DOI":"10.1007\/BFb0070929"},{"key":"ref_6","first-page":"101","article-title":"Towards classification of simple finite dimensional modular Lie superalgebras","volume":"3","author":"Leites","year":"2007","journal-title":"J. Prime Res. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/00927870500346065","article-title":"The Cartan-type modular Lie superalgebra KO","volume":"34","author":"Fu","year":"2006","journal-title":"Commun. Algebra"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1142\/S021919970900351X","article-title":"Finite-dimensional special odd Hamiltonian superalgebras in prime characteristic","volume":"11","author":"Liu","year":"2009","journal-title":"Commun. Contemp. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.jalgebra.2003.10.019","article-title":"The derivation algebra of the Cartan-type Lie superalgebra HO","volume":"273","author":"Liu","year":"2004","journal-title":"J. Algebra"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1016\/j.jpaa.2009.11.010","article-title":"Infinite-dimensional modular special odd contact superalgebras","volume":"214","author":"Mu","year":"2010","journal-title":"J. Pure Appl. Algebra"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1007\/BF03186962","article-title":"Finite-dimensional Lie superalgebras of Cartan type over fields of prime characteristic","volume":"42","author":"Zhang","year":"1997","journal-title":"Chin. Sci. Bull."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1016\/j.jalgebra.2010.04.032","article-title":"Restricted representations of the Witt superalgebras","volume":"324","author":"Shu","year":"2010","journal-title":"J. Algebra"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1016\/j.jpaa.2012.01.010","article-title":"Derivations of the even part of contact Lie superalgebra","volume":"216","author":"Guan","year":"2012","journal-title":"J. Pure Appl. Algebra"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1080\/03081087.2018.1465525","article-title":"Biderivations and linear commuting maps on the restricted Cartan-type Lie algebras W(n; 1\u0332) and S(n; 1\u0332)","volume":"67","author":"Chang","year":"2019","journal-title":"Linear Multilinear Algebra"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1080\/00927872.2018.1503286","article-title":"Biderivations and linear commuting maps on the restricted Cartan-type Lie algebras H(n; 1\u0332)","volume":"47","author":"Chang","year":"2019","journal-title":"Commun. Algebra"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.13001\/1081-3810.3100","article-title":"Biderivations and linear commuting maps on simple generalized Witt algebras over a field","volume":"31","author":"Chen","year":"2016","journal-title":"Electron. J. Linear Algebra"},{"key":"ref_17","first-page":"777","article-title":"Linear commuting maps and biderivations on the Lie algebras W(a, b)","volume":"26","author":"Han","year":"2016","journal-title":"J. Lie Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1080\/03081087.2017.1295433","article-title":"Biderivations of finite-dimensional complex simple Lie algebras","volume":"66","author":"Tang","year":"2018","journal-title":"Linear Multilinear Algebra"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4097","DOI":"10.1080\/00927872.2010.517820","article-title":"Biderivations of the parabolic subalgebras of simple Lie algebras","volume":"39","author":"Wang","year":"2011","journal-title":"Commun. Algebra"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2166","DOI":"10.1080\/00927872.2012.654551","article-title":"Biderivations and linear commuting maps on the Schr\u00f6dinger-Virasoro Lie algebra","volume":"41","author":"Wang","year":"2013","journal-title":"Commun. Algebra"},{"key":"ref_21","first-page":"361","article-title":"Commuting maps: A survey","volume":"8","year":"2004","journal-title":"Taiwan J. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1080\/03081087.2016.1167815","article-title":"Super-biderivations of Lie superalgebras","volume":"65","author":"Fan","year":"2017","journal-title":"Linear Multilinear Algebra"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5342","DOI":"10.1080\/00927872.2016.1172617","article-title":"Linear super-commuting maps and super-biderivations on the super-Virasoro algebras","volume":"44","author":"Xia","year":"2016","journal-title":"Commun. Algebra"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5076","DOI":"10.1080\/00927872.2020.1778715","article-title":"Super-biderivations and linear super-commuting maps on the Lie superalgebras","volume":"48","author":"Tang","year":"2020","journal-title":"Commun. Algebra"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00010-017-0503-x","article-title":"Super-biderivations of classical simple Lie superalgebras","volume":"92","author":"Yuan","year":"2018","journal-title":"Aequationes Math."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Dilxat, M., Gao, S.L., and Liu, D. (2022). Super-biderivations and post-Lie superalgebras on some Lie superalgebras. arXiv.","DOI":"10.1007\/s10114-023-1019-z"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1080\/03081087.2019.1593312","article-title":"Super-biderivations of the generalized Witt Lie superalgebra W(m, n; t\u0332)","volume":"69","author":"Chang","year":"2021","journal-title":"Linear Multilinear Algebra"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3237","DOI":"10.1080\/00927872.2020.1731822","article-title":"Super-biderivations of the contact Lie superalgebra K(m, n; t\u0332)","volume":"48","author":"Zhao","year":"2020","journal-title":"Commun. Algebra"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/12\/1108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:35:17Z","timestamp":1760132117000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/12\/1108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,8]]},"references-count":28,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["axioms12121108"],"URL":"https:\/\/doi.org\/10.3390\/axioms12121108","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,12,8]]}}}