nLab Victor Kac

• wikipedia page

Selected writings

On super Lie algebras, Jordan superalgebras:

• Victor Kac, Lie superalgebras, Advances in Math. 26 1 (1977) 8-96 [doi:10.1016/0001-8708(77)90017-2]

• Victor Kac: A sketch of Lie superalgebra theory, Comm. Math. Phys. 53 1 (1977) 31-64 [euclid:1103900590, doi:10.1007/BF01609166]

• Victor Kac, Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5 (1977), 1375–1400, (doi: 10.1080/00927877708822224)

See also:

• The idea of locality [q-alg/9709008]

On affine Lie algebras:

• Victor G. Kac, Infinite Dimensional Lie Algebras, Progress in Mathematics 44 Springer 1983 [doi:10.1007/978-1-4757-1382-4), Cambridge University Press (1990) [doi:10.1017/CBO9780511626234]

their relation to modular forms:

• Victor G. Kac, Dale H. Peterson, Affine Lie algebras and Hecke modular forms, Bull. Amer. Math. Soc. (N.S.) 3 3 (1980) 1057-1061 [bams:1183547694]

• Victor G. Kac, Dale H. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Advances in Mathematics 53 2 (1984) 125-264 [doi:10.1016/0001-8708(84)90032-X]

• Victor G. Kac, Minoru Wakimoto, Modular and conformal invariance constraints in representation theory of affine algebras, Advances in Mathematics 70 2 (1988) 156-236 [doi:10.1016/0001-8708(88)90055-2, spire:275458]

On non-integrable but “admissible” irreps of affine Lie algebras (cf. fractional level WZW models):

• Victor G. Kac, Minoru Wakimoto, Modular invariant representations of infinite-dimensional Lie algebras and superalgebras, PNAS 85 14 (1988) 4956-4960 [doi:10.1073/pnas.85.14.4956]

• Victor G. Kac, Minoru Wakimoto, Classification of modular invariant representations of affine algebras, p. 138-177 in V. G. Kač (ed.): Infinite dimensional Lie algebras and groups, Advanced series in Mathematical physics 7, World Scientific (1989) [pdf, cds:268092]

On vertex operator algebras:

• Victor Kac, Vertex algebras for beginners, Amer. Math. Soc., Univ. Lecture Series 10 (1998) [ams:ulect-10-r, ZMATH entry]

On vertex operator algebras over non-archimedean fields:

• Victor Kac, Non-Archimedean vertex algebras [arXiv:2304.09651]

On Poisson vertex algebras and integrability of Hamiltonian PDEs:

• Alberto De Sole, Victor G. Kac, Daniele Valeri, Poisson vertex algebras and Hamiltonian PDE, in Encyclopedia of Mathematical Physics 2nd ed, Elsevier (2024) [arXiv:2306.09709]

category: people