Canonical Bases of Borcherds-Cartan Type
Yiqiang Li, Zongzhu Lin
TL;DR
This paper investigates the canonical bases of quantum generalized Kac-Moody algebras linked to Borcherds-Cartan matrices, establishing conditions under which bases coincide and addressing a question by Lusztig.
Contribution
It proves that canonical bases coincide for algebras defined by different matrices when the algebras are identical, partially answering Lusztig's question.
Findings
Canonical bases coincide when the associated algebras are the same.
Conditions under which different matrices produce the same algebra are identified.
Partially answers Lusztig's question regarding canonical bases.
Abstract
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. We show that the canonical bases coincide provided that the algebras coincide. We also answer partially a question by Lusztig.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons