A Short Course in Differential Geometry and Topology by A. T. Fomenko

By A. T. Fomenko

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14, pp. 171–199. Clay Mathematics Institute (2010) 21. : Lie prealgebras. In: Connes, A. et al. ), Noncommutative Geometry and Global Analysis, Contemporary Mathematics, vol. 546, pp. 115–135. American Mathematical Society (2011) 22. : PWB-deformations of N -Koszul algebras. J. Algebra 302, 116–155 (2006) 23. : Calabi-Yau algebras. AG/0612139 24. : Algebraic aspects of the quantum Yang-Baxter equation. Algebra i Analiz (Transl. in Leningrad Math. J. 2 801–828 (1991)), 2, 119–148 (1990) 25. : Higher Koszul algebras and A-infinity algebras.

Karolinsky et al. is known as the classical Kostant’s problem, see [6, 7, 12, 15, 16]. The complete answer to it is still unknown even in the q = 1 case. However, there are examples of α for which the action map U (g) ⊕ End L(α) fin is not surjective. Such examples exist even in the case g is of type A [17]. The main idea of our approach to Kostant’s problem, both in the Lie-algebraic and quantum group cases, is that End L(α) fin has two other presentations. First, it follows from the results of [11] that End L(α) fin is canonically isomorphic to HomU L(α), L(α) ≥ F , where U is U (g) (resp.

Dubois-Violette 16. : Yang-Mills and some related algebras. In: Rigorous Quantum Field Theory, Progress in Mathematics, vol. 251, pp. 65–78. Birkhaüser (2007) 17. : Noncommutative finite-dimensional manifolds. II. Moduli space and structure of noncommutative 3-spheres. Commun. Math. Phys. 281(1), 23–127 (2008) 18. : Graded algebras and multilinear forms. C. R. Acad. Sci. Paris Ser. I 341, 719–724 (2005) 19. : Multilinear forms and graded algebras. J. Algebra 317, 198–225 (2007) 20. : Noncommutative coordinate algebras.

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