Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g wi...Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.展开更多
The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified,respectively.We prove that any unitary irreducible module of...The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified,respectively.We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form Aa,b,c for a ∈ R,6∈1/2+√-1R and c∈C.展开更多
Let■be a compatible total order on the additive group Z^2,and L be the rank two HeisenbergVirasoro algebra.For any c=(c1,c2,c3,c4)∈C^4,we define a Z^2-graded Verma module M(c,■)for L.A necessary and sufficient cond...Let■be a compatible total order on the additive group Z^2,and L be the rank two HeisenbergVirasoro algebra.For any c=(c1,c2,c3,c4)∈C^4,we define a Z^2-graded Verma module M(c,■)for L.A necessary and sufficient condition for M(c,■)to be irreducible is provided.Moreover,the maximal Z^2-graded submodules of M(c,■)are characterized when M(c,■)is reducible.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11531004 and 11701183)the Fundamental Research Funds for the Central Universities(Grant No.20720190069)the Simons Foundation(Grant No.198129)。
文摘Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.
基金Supported by the National Natural Science Foundation of China(Nos.11571145,11531004,11471333 and 11471268).
文摘The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified,respectively.We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form Aa,b,c for a ∈ R,6∈1/2+√-1R and c∈C.
基金supported by National Natural Science Foundation of China(Grant Nos.11471268 and 11531004)。
文摘Let■be a compatible total order on the additive group Z^2,and L be the rank two HeisenbergVirasoro algebra.For any c=(c1,c2,c3,c4)∈C^4,we define a Z^2-graded Verma module M(c,■)for L.A necessary and sufficient condition for M(c,■)to be irreducible is provided.Moreover,the maximal Z^2-graded submodules of M(c,■)are characterized when M(c,■)is reducible.
