Canonical bases of Borcherds-Cartan type

Yiqiang Li; Zongzhu Lin

doi:10.1017/S0027763000009661

Canonical bases of Borcherds-Cartan type

Yiqiang Li
, Zongzhu Lin

Mathematics

Kansas State University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study the canonical basis for the negative part U^- of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras U^- associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U^- coincide (Theorem 6.3.5). We also answer partially a question by Lusztig in [L3] (Theorem 7.1.1).

Original language	English
Pages (from-to)	169-193
Number of pages	25
Journal	Nagoya Mathematical Journal
Volume	194
DOIs	https://doi.org/10.1017/S0027763000009661
State	Published - 2009

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title = "Canonical bases of Borcherds-Cartan type",

abstract = "We study the canonical basis for the negative part U- of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras U- associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U- coincide (Theorem 6.3.5). We also answer partially a question by Lusztig in [L3] (Theorem 7.1.1).",

author = "Yiqiang Li and Zongzhu Lin",

year = "2009",

doi = "10.1017/S0027763000009661",

language = "English",

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journal = "Nagoya Mathematical Journal",

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AU - Li, Yiqiang

AU - Lin, Zongzhu

PY - 2009

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N2 - We study the canonical basis for the negative part U- of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras U- associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U- coincide (Theorem 6.3.5). We also answer partially a question by Lusztig in [L3] (Theorem 7.1.1).

AB - We study the canonical basis for the negative part U- of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras U- associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U- coincide (Theorem 6.3.5). We also answer partially a question by Lusztig in [L3] (Theorem 7.1.1).

UR - https://www.scopus.com/pages/publications/69549096104

U2 - 10.1017/S0027763000009661

DO - 10.1017/S0027763000009661

M3 - Article

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SN - 0027-7630

VL - 194

SP - 169

EP - 193

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

ER -

Canonical bases of Borcherds-Cartan type

Abstract

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