一类李代数的泛中心扩张
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摘要
高秩loop-Witt代数是一类常见的李代数,在实际生活中有非常重要的作用。本文构造了高秩loop-Witt代数的泛中心扩张,在二维环面上的导子代数展开研究,进一步丰富了高维环面导子代数的子代数结构及内容。
引文
[1]曾波.量子环面上一类李代数的导子和中心扩张[J].数学学报,2009,52(1):165-172.
[2]RAO S E. Inrreducible representations of the Lie-algebra of the Diffeomorphisms of a d-dimensional torus[J].Journal of Algebra,1996,182:401-421.
[3]XUE M,LIN W,TAN S. Central extension,derivations and automorphism group for Lie algebras arising from 2-dimensional tous[J]. J. Lie Theory,2006,16(1):139-153.
[4]LIN W,TAN S. Central extensions and derivations of the Lie algebras of skew derivations for the quantum torus[J]. Communications in Algebra,2005,33(11):3919-3938.
[5]李颖.一类李代数的结构及表示[D].哈尔滨:黑龙江大学,2013:1-12.
[6]TANG X M. Subalgebras of the Lie algebra of the derivations on a torus and their representations[J]. Algebra Colloquium,2012,19(4):615-630.
[7]CHEN Z. Biderivations and linear commuting maps on simple generalized Witt algebras over afield[J]. Electron J Linear Algebra,2016,31(1):1-12.
[8]HAN X,WANG D,XIA C. Linear commuting maps and biderivations on the Lie algebras W(a,b)[J]. J Lie Theory,2016,26(3):777-786.
[9]XIA C,WANG D,HAN X. Linear super-commuting maps and super-biderivations on the super-Virasoro algebras[J]. Commum Algebra,2016,44(12):5342-5350.
[10]FAN G,DAI X. Supei-biderivations of Lie superalgebras[J]. Linear Multilinear Algebra,2017,65(1):58-66.
[11]BOUNDS J. Commuting maps over the ring of strictly upper triangular matrices[J]. Linear Algebra Appl,2016,507:132-136.
[2]RAO S E. Inrreducible representations of the Lie-algebra of the Diffeomorphisms of a d-dimensional torus[J].Journal of Algebra,1996,182:401-421.
[3]XUE M,LIN W,TAN S. Central extension,derivations and automorphism group for Lie algebras arising from 2-dimensional tous[J]. J. Lie Theory,2006,16(1):139-153.
[4]LIN W,TAN S. Central extensions and derivations of the Lie algebras of skew derivations for the quantum torus[J]. Communications in Algebra,2005,33(11):3919-3938.
[5]李颖.一类李代数的结构及表示[D].哈尔滨:黑龙江大学,2013:1-12.
[6]TANG X M. Subalgebras of the Lie algebra of the derivations on a torus and their representations[J]. Algebra Colloquium,2012,19(4):615-630.
[7]CHEN Z. Biderivations and linear commuting maps on simple generalized Witt algebras over afield[J]. Electron J Linear Algebra,2016,31(1):1-12.
[8]HAN X,WANG D,XIA C. Linear commuting maps and biderivations on the Lie algebras W(a,b)[J]. J Lie Theory,2016,26(3):777-786.
[9]XIA C,WANG D,HAN X. Linear super-commuting maps and super-biderivations on the super-Virasoro algebras[J]. Commum Algebra,2016,44(12):5342-5350.
[10]FAN G,DAI X. Supei-biderivations of Lie superalgebras[J]. Linear Multilinear Algebra,2017,65(1):58-66.
[11]BOUNDS J. Commuting maps over the ring of strictly upper triangular matrices[J]. Linear Algebra Appl,2016,507:132-136.