Computing of the number of right coideal subalgebras of Uq(so(2n+1))

Autor(es)

Kharchenko, V. K. ^{[1, 2]} ; Sagahon, A. V. Lara ^[2] ; Rivera, J. L. Garza ^[2]

Afiliação do(s) autor(es)

^[1] Sobolev Inst Math, Novosibirsk - Russia

^[2] Univ Nacl Autonoma Mexico, FES Cuautitlan, Mexico City 04510, DF - Mexico

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 341, n. 1, p. 279-296, SEP 1 2011.
• Citações Web of Science: 3

Resumo

In this paper we complete the classification of right coideal sub-algebras containing all grouplike elements for the multiparameter version of the quantum group Uq(so(2n+1)), q(t) not equal 1. It is known that every such subalgebra has a triangular decomposition U = U(-)HU(+), where U(-) and U(+) are right coideal subalgebras of negative and positive quantum Bore! subalgebras. We found a necessary and sufficient condition for the above triangular composition to be a right coideal subalgebra of U(q)(so(2n+1)) in terms of the PBW-generators of the components. Furthermore, an algorithm is given that allows one to find an explicit form of the generators. Using a computer realization of that algorithm, we determined the number r(n) of different right coideal subalgebras that contain all grouplike elements for n <= 7. If q has a finite multiplicative order t > 4, the classification remains valid for homogeneous right coideal subalgebras of the multiparameter version of the Lusztig quantum group u(q)(so(2n+1)) (the Frobenius-Lusztig kernel of type B(n)) in which case the total number of homogeneous right coideal subalgebras and the particular generators are the same. (C) 2011 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 10/51952-3 - Vladislav Kharchenko | Universidad Nacional Autónoma de México - México
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional