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- W2952427942 abstract "In this paper, we develop the crystal basis theory for quantum generalized Kac-Moody algebras. For a quantum generalized Kac-Moody algebra $U_q(mathfrak g)$, we first introduce the category $mathcal O_{int}$ of $U_q(mathfrak g)$-modules and prove its semisimplicity. Next, we define the notion of crystal bases for $U_q(mathfrak g)$-modules in the category $mathcal O_{int}$ and for the subalgebra $U_q^-(mathfrak g)$. We then prove the tensor product rule and the existence theorem for crystal bases. Finally, we construct the global bases for $U_q(mathfrak g)$-modules in the category $mathcal O_{int}$ and for the subalgebra $U_q^-(mathfrak g)$." @default.
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- W2952427942 date "2003-05-28" @default.
- W2952427942 modified "2023-10-18" @default.
- W2952427942 title "Crystal Bases for Quantum Generalized Kac-Moody Algebras" @default.
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