English

Two-parameter quantum algebras, canonical bases and categorifications

Representation Theory 2013-11-06 v2 Quantum Algebra

Abstract

A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse sheaves and Deligne's weight theory based on Lusztig's work. A categorification of the negative part of a two-parameter quantum algebra is provided. A two-parameter quantum algebra is shown to be a two-cocycle deformation, depending only on the second parameter, of its one-parameter analogue.

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Cite

@article{arxiv.1303.2429,
  title  = {Two-parameter quantum algebras, canonical bases and categorifications},
  author = {Zhaobing Fan and Yiqiang Li},
  journal= {arXiv preprint arXiv:1303.2429},
  year   = {2013}
}

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Reference updated

R2 v1 2026-06-21T23:39:45.864Z