We investigate the quantization problem of $(-1)$-shifted derived Poisson manifolds in terms $\BV_\infty$-operators on space Berezinian half-densities. prove that quantizing such a manifold is equivalent to lifting consecutive sequences Maurer-Cartan elements short exact differential graded Lie algebras, where obstruction certain class second cohomology. Consequently, quantizable if cohomology ...

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p, q) of the Cartan series Al and the pseudo-unitary algebras u(p, q), are completely determined and classified for arbitrary p, q. In addition to the su(p, q) and u(p, q) algebras, whose second cohomology group is well known to be trivi...

This leads to two ways to construct the ring cohomology: cohomology for rings which are regarded as algebras due to Shukla [Sh], and ring cohomology due to Mac Lane [Mac]. The ring structure has been categorized by the definition of an Ann-category [4]. Each congruence class of Ann-categories is characterized by a cohomology class of structures (Theorem 4.3[4]). For regular Ann-categories, this...

For a positive integer n we introduce quadratic Lie algebras trn qtr n and discrete groups Trn, QTr n naturally associated with the classical and quantum Yang-Baxter equation, respectively. We prove that the universal enveloping algebras of the Lie algebras trn, qtr n are Koszul, and compute their Hilbert series. We also compute the cohomology rings of these Lie algebras (which by Koszulity are...

We prove that some skew group algebras have Noetherian cohomology rings, a property inherited from their component parts. The proof is an adaptation of Evens’ proof of finite generation of group cohomology. We apply the result to a series of examples of finite dimensional Hopf algebras in positive characteristic.

Let Oλ be a generic coadjoint orbit of a compact semi-simple Lie group K. Weight varieties are the symplectic reductions of Oλ by the maximal torus T in K. We use a theorem of Tolman and Weitsman to compute the cohomology ring of these varieties. Our formula relies on a Schubert basis of the equivariant cohomology of Oλ, and it makes explicit the dependence on λ and a parameter in Lie(T )∗ =: t∗.