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Soc."],"abstract":"<p>There is a natural way to associate to the commuting variety <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C left-parenthesis upper A right-parenthesis\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>C<\/mml:mi>\n      <mml:mo stretchy=\"false\">(<\/mml:mo>\n      <mml:mi>A<\/mml:mi>\n      <mml:mo stretchy=\"false\">)<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">C(A)<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> of an algebra <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n  <mml:semantics>\n    <mml:mi>A<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> a module over a polynomial ring. It serves as a vehicle to study the arithmetical properties of <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C left-parenthesis upper A right-parenthesis\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>C<\/mml:mi>\n      <mml:mo stretchy=\"false\">(<\/mml:mo>\n      <mml:mi>A<\/mml:mi>\n      <mml:mo stretchy=\"false\">)<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">C(A)<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>, particularly Cohen-Macaulayness. The focus here is on Lie algebras and some of their representations.<\/p>","DOI":"10.1090\/s0002-9947-1990-0958883-0","type":"journal-article","created":{"date-parts":[[2012,6,6]],"date-time":"2012-06-06T16:40:46Z","timestamp":1339000846000},"page":"183-196","source":"Crossref","is-referenced-by-count":6,"title":["The Jacobian module of a Lie algebra"],"prefix":"10.1090","volume":"321","author":[{"given":"J. P.","family":"Brennan","sequence":"first","affiliation":[]},{"given":"M. V.","family":"Pinto","sequence":"additional","affiliation":[]},{"given":"W. V.","family":"Vasconcelos","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1990]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/0021-8693(81)90357-4","article-title":"Complete intersections and symmetric algebras","volume":"73","author":"Avramov, Luchezar L.","year":"1981","journal-title":"J. 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