{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:08:31Z","timestamp":1762952911796,"version":"3.45.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Noncommut. Geom."],"accepted":{"date-parts":[[2021,5,5]]},"published-print":{"date-parts":[[2021,12,7]]},"abstract":"<jats:p>\n                    For each nonzero\n                    <jats:inline-formula>\n                      <jats:tex-math>h\\in\\mathbb{F}[x]<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbb{F}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is a field, let\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{A}_h<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    be the unital associative algebra generated by elements\n                    <jats:inline-formula>\n                      <jats:tex-math>x,y<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , satisfying the relation\n                    <jats:inline-formula>\n                      <jats:tex-math>yx-xy=h<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . This gives a parametric family of subalgebras of the Weyl algebra\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{A}_1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , containing many well-known algebras which have previously been studied independently. In this paper, we give a full description of the Hochschild cohomology\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{\\mathsf{HH}}^{\\bullet}(\\mathsf{A}_h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    over a field of an arbitrary characteristic. In case\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbb{F}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    has a positive characteristic, the center\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{Z}(\\mathsf{A}_{h})<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    of\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{A}_h<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is nontrivial and we describe\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{\\mathsf{HH}}^\\bullet(\\mathsf{A}_h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    as a module over\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{Z}(\\mathsf{A}_{h})<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . The most interesting results occur when\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbb{F}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    has a characteristic\n                    <jats:inline-formula>\n                      <jats:tex-math>0<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In this case, we describe\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{\\mathsf{HH}}^\\bullet(\\mathsf{A}_h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    as a module over the Lie algebra\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{\\mathsf{HH}}^1(\\mathsf{A}_h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and find that this action is closely related to the intermediate series modules over the Virasoro algebra. We also determine when\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{\\mathsf{HH}}^\\bullet(\\mathsf{A}_h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is a semisimple\n                    <jats:inline-formula>\n                      <jats:tex-math>\\operatorname{\\mathsf{HH}}^1(\\mathsf{A}_h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -module.\n                  <\/jats:p>","DOI":"10.4171\/jncg\/439","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T17:45:14Z","timestamp":1638899114000},"page":"1373-1407","source":"Crossref","is-referenced-by-count":2,"title":["Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra"],"prefix":"10.4171","volume":"15","author":[{"given":"Samuel A.","family":"Lopes","sequence":"first","affiliation":[{"name":"Universidade do Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1770-4568","authenticated-orcid":false,"given":"Andrea","family":"Solotar","sequence":"additional","affiliation":[{"name":"Universidad de Buenos Aires, Argentina"}]}],"member":"2673","container-title":["Journal of Noncommutative Geometry"],"original-title":[],"link":[{"URL":"https:\/\/www.ems-ph.org\/fulltext\/10.4171\/JNCG\/439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:04:02Z","timestamp":1762952642000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/jncg\/439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,7]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.4171\/jncg\/439","relation":{},"ISSN":["1661-6952","1661-6960"],"issn-type":[{"type":"print","value":"1661-6952"},{"type":"electronic","value":"1661-6960"}],"subject":[],"published":{"date-parts":[[2021,12,7]]}}}