相关论文: Addendum to ``Canonical bases for quantum generali…

We construct a canonical basis for quantum generalized Kac-Moody algebra via semisimple perverse sheaves on varieties of representations of quivers. We compare this basis with the one recently defined purely algebraically by Jeong, Kang and…

This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.

We study the canonical basis for the negative part of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras associated to two different matrices satisfying certain conditions may coincide.…

In this paper we extend several results about root systems of Kac-Moody algebras to superalgebra context. In particular, we describe the root bases and the sets of imaginary roots.

We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

In this paper, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem and give a characterization of the crystals…

Given any quantum cluster algebra arising from a quantum unipotent subgroup of symmetrizable Kac-Moody type, we verify the quantization conjecture in full generality that the quantum cluster monomials are contained in the dual canonical…

We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic…

This set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type.

In this article, we develop an algebraic framework of axioms which abstracts various high-level properties of multi-qudit representations of generalized Clifford algebras. We further construct an explicit model and prove that it satisfies…

In this paper, the singular Ringel-Hall algebra for a tame quiver is introduced and shown to be isomorphic to the positive part of the quantum extended Kac-Moody algebra. A PBW basis is constructed and a new class of perverse sheaves is…

We introduce quantum monadic and quantum cylindric algebras. These are adaptations to the quantum setting of the monadic algebras of Halmos, and cylindric algebras of Henkin, Monk and Tarski, that are used in algebraic treatments of…

We construct a canonical basis for a class of tensor product modules of a quantum covering group associated to a Kac-Moody Lie superalgebra of anisotropic type, and use these bases to construct a canonical basis for the modified form of a…

Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized…

This text provides an introduction and complements to some basic constructions and results in 2-representation theory of Kac-Moody algebras.

The first goal of this paper is to study the amount of compatibility between two important constructions in the theory of quantized enveloping algebras, namely the canonical basis and the quantum Frobenius morphism. The second goal is to…

We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of $q$ and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.

In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

We extend results for the K-theory of Hecke algebras of reductive $p$-adic groups to completed Kac-Moody groups.