Generalized root systems and the affine Lie superalgebra $${\mathrm {G}}^{(1)}(3)$$
Tóm tắt
We give a new proof of the presentation of the affine Lie superalgebra
$${\mathrm {G}}^{(1)}(3)$$
using a Weyl groupoid.
Tài liệu tham khảo
Azam, S., Yamane, H., Yousofzadeh, M.: Classification of finite dimensional irreducible representations of generalized quantum groups via Weyl groupoids. Publ. Res. Inst. Math. Sci. 51(1), 59–130 (2015)
Cuntz, M., Heckenberger, I.: Weyl groupoids with at most three objects. J. Pure Appl. Algebra 213(6), 1112–1128 (2009)
Heckenberger, I., Yamane, H.: A generalization of Coxeter groups, root systems, and Matsumoto’s theorem. Math. Z. 259, 255–276 (2008)
Kac, V.G.: Lie superalgebras. Adv. Math. 26(1), 8–96 (1977)
Kac, V.G.: Infinite-Dimensional Lie Algebras, 3rd edn. Cambridge University Press, Cambridge (1990)
Yamane, H.: Universal \(R\)-matrices for quantum groups associated to simple Lie superalgebras. Proc. Jpn. Acad. Ser. A Math. Sci. 67(4), 108–112 (1991)
Yamane, H.: Quantized enveloping algebras associated with simple Lie superalgebras and their universal \(R\)-matrices. Publ. Res. Inst. Math. Sci. 30(3), 15–87 (1994)
Yamane, H.: A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras. Proc. Jpn. Acad. Ser. A Math. Sci. 70(1), 31–36 (1994)
Yamane, H.: On defining relations of affine Lie superalgebras and affine quantized universal enveloping superalgebras. Publ. RIMS Kyoto Univ. 35(3), 321–390 (1999)
Yamane, H.: Errata to: “On defining relations of affine Lie superalgebras and affine quantized universal enveloping superalgebras”. Publ. Res. Inst. Math. Sci. 37(4), 615–619 (2001)