Classification of simple bounded weight modules of the Lie algebra of vector fields on ℂn
Tóm tắt
Từ khóa
Tài liệu tham khảo
Y. Billig and V. Futorny, Classification of irreducible representations of Lie algebra of vector fields on a torus, Journal für die Reine und Angewandte Mathematik 720 (2016), 199–216.
Y. Billig and V. Futorny, Classification of simple bounded weight modules for solenoidal Lie algebras. Israel Journal of Mathematics 222 (2017), 109–123.
Y. Billig, A. Molev and R. Zhang, Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus, Advances in Mathematics 218 (2008), 1972–2004.
A. Cavaness and D. Grantcharov, Bounded weight modules of the Lie algebra of vector fields on ℂ2, Journal of Algebra and its Applications 16 (2017), Article no. 1750236.
S. Eswara Rao, Irreducible representations of the Lie-algebra of the diffeomorphisms of a d-dimensional torus, Journal of Algebra 182 (1996), 401–421.
S. Eswara Rao, Partial classification of modules for Lie algebra of diffeomorphisms of d-dimensional torus, Journal of Mathematical Physics 45 (2004), 3322–3333.
V. Futorny, D. Grantcharov and V. Mazorchuk, Weight modules over infinite-dimensional Weyl algebras, Proceedings of the American Mathematical Society 142 (2014), 3049–3057.
D. Grantcharov and V. Serganova, Cuspidal representations of $$\left(\mathfrak{s}\mathfrak{l} {n + 1} \right)$$, Advances in Mathematics 224 (2010) 1517–1547.
V. G. Kac, Some problems of infinite-dimensional Lie algebras and their representations, in Lie Algebras and Related Topics, Lecture Notes in Mathematics, Vol. 933, Springer, Berlin, 1982, pp. 117–126.
T. A. Larsson, Conformal fields: A class of representations of Vect(N), International Journal of Modern Physics. A 7 (1992), 6493–6508.
G. Liu, R. Lu and K. Zhao, Irreducible Witt modules from Weyl modules and $${\mathfrak{g}\mathfrak{l}_n}$$ modules, Journal of Algebra 511 (2018), 164–181.
D. Liu, Y. Pei and L. Xia, Classification of simple weight modules for the N = 2 superconformal algebra, https://arxiv.org/abs/1904.08578.
R. Lü and Y. Xue, Bounded weight modules over the Lie superalgebra of Cartan W-type, Algebras and Representation Theory, https://doi.org/10.1007/s10468-021-10112-3.
R. Lu and K. Zhao, Classification of irreducible weight modules over higher rank Virasoro algebras, Advances in Mathematics 201 (2006), 630–656.
O. Mathieu, Classification of Harish-Chandra modules over the Virasoro algebras, Inventions Mathematica 107 (1992), 225–234.
V. Mazorchuk and C. Stroppel, Cuspidal $${\mathfrak{s}\mathfrak{l}_n}$$ modules and deformations of certain Brauer tree algebras, Advances in Mathematics 228 (2011), 1008–1042.
V. Mazorchuk and K. Zhao, Supports of weight modules over Witt algebras, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 141 (2011), 155–170.
I. Penkov and V. Serganova, Weight representations of the polynomial Cartan type Lie algebras W n and S n, Mathematical Research Letters 6 (1999), 397–416.
A. N. Rudakov, Irreducible representations of infinite-dimensional Lie algebras of Cartan type, Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 38 (1974), 835–866 (Russian); English translation: Mathematics of the USSR-Izvestiya 8 (1974), 836–866.
A. N. Rudakov, Irreducible representations of infinite-dimensional Lie algebras of types S and H, Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 39 (1975), 496–511; English translation: Mathematics of the USSR-Izvestiya 9 (1975), 465–480.
G. Shen, Graded modules of graded Lie algebras of Cartan type. I. Mixed products of modules, Scientia Sinica. Series A. Mathematical, Physical, Astronomical & Technical Sciences 29 (1986), 570–581.
Y. Su, Simple modules over the high rank Virasoro algebras, Communications in Algebra 29 (2001), 2067–2080.