ISSN:
1572-9079
Keywords:
Borel subalgebra
;
quantum groups
;
linear algebra
;
homological functors
;
representation theory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Both building upon and revising previous literature, this paper formulates the general notion of a Borel subalgebra B of a quasi-hereditary algebra A. We present various general constructions of Borel subalgebras, establish a triangular factorization of A, and relate the concept to graded Kazhdan–Lusztig theories in the sense of Cline et al. (Tôhoku Math. J. 45 (1993), 511–534). Various interesting types of Borel subalgebras arise naturally in different contexts. For example, `excellent" Borel subalgebras come about by abstracting the theory of Schubert varieties. Numerous examples from algebraic groups, q-Schur algebras, and quantum groups are considered in detail.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009980101091
