Quadratic linear algebras associated with factorizations of noncommutative polynomials and noncommutative differential polynomials
✍ Scribed by I. Gelfand; V. Retakh; R. L. Wilson
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2001
- Tongue
- English
- Weight
- 333 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1022-1824
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📜 SIMILAR VOLUMES
The quadratic algebras Q n are associated with pseudo-roots of noncommutative polynomials. We compute the Hilbert series of the algebras Q n and of the dual algebras Q ! n .
We study Hochschild homology and cohomology for a class of noncommutative polynomial algebras which are both quantum (in the sense that they contain some copies of Manin's quantum plane as subalgebras) and classical (in the sense that they also contain some copies of the Weyl algebra A1). We obtain
we show that the system S = 1, B = 2n + 2sy + y2 has the algebraic solution h(z, v) = Zf,,(z)y + 2nH,,-i(r), where'H,,(r) is the Hermite polynomial of degree n, and the system is not Darboux integrable and has no Darboux integrating factor for any n E N.