## Construction of the affine Lie algebra $$A^{(1)}_1$$.(English)Zbl 0388.17006

### MSC:

 17B65 Infinite-dimensional Lie (super)algebras
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### References:

 [1] Feingold, A., Lepowsky, J.: The Weyl-Kac character formula and power series identities (to appear) · Zbl 0391.17009 [2] Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Inventiones math.34, 37–76 (1976) · Zbl 0358.17015 [3] Kac, V.: Simple irreducible graded Lie algebras of finite growth (in Russian). Izv. Akad. Nauk SSSR32, 1323–1367 (1968); English translation: Math. USSR-Izv.2, 1271–1311 (1968) [4] Kac, V.: Infinite-dimensional Lie algebras and Dedekind’s {$$\eta$$}-function (in Russian). Funkt. Anal. Ego Prilozheniya8, 77–78 (1974); English translation: Funct. Anal. Appl.8, 68–70 (1974) · Zbl 0298.57019 [5] Kac, V.: Infinite-dimensional algebras, Dedekind’s {$$\eta$$}-function, classical Möbius function, and the very strange formula. Advan. Math. (to appear) · Zbl 0391.17010 [6] Kac, V., Kazhdan, D., Lepowsky, J., Wilson, R.: (manuscript in preparation) [7] Lepowsky, J.: Generalized Verma modules, loop space cohomology, and Macdonald-type identities (to appear) · Zbl 0414.17007 [8] Lepowsky, J., Milne, S.: Lie algebraic approaches to classical partition identities. Advan. Math. (to appear) · Zbl 0384.10008 [9] Moody, R.: A new class of Lie algebras. J. Algebra10, 211–230 (1968) · Zbl 0191.03005 [10] Schwartz, J.: Dual resonance theory. Phys. Rept.8C, 269–335 (1973)
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