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Computing of the number of right coideal subalgebras of
- Source :
-
Journal of Algebra . Sep2011, Vol. 341 Issue 1, p279-296. 18p. - Publication Year :
- 2011
-
Abstract
- Abstract: In this paper we complete the classification of right coideal subalgebras containing all grouplike elements for the multiparameter version of the quantum group , . It is known that every such subalgebra has a triangular decomposition , where and are right coideal subalgebras of negative and positive quantum Borel subalgebras. We found a necessary and sufficient condition for the above triangular composition to be a right coideal subalgebra of 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 of different right coideal subalgebras that contain all grouplike elements for . If q has a finite multiplicative order , the classification remains valid for homogeneous right coideal subalgebras of the multiparameter version of the Lusztig quantum group (the Frobenius–Lusztig kernel of type ) in which case the total number of homogeneous right coideal subalgebras and the particular generators are the same. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 341
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 63185370
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2011.06.018