Showing papers by "Valery A. Lunts published in 2022"
TL;DR: In this article, it was shown that the lattice of triangulated subcategories in D b ( R N − mod ) has a rich structure, in contrast to zero-dimensional complete intersections.
1 citations
25 Jul 2022
TL;DR: In this paper , an explicit Sn-equivariant bijection between the integral points in a certain zonotope in R, combinatorially equivalent to the permutahedron, and the set of m-parking functions of length n was found.
Abstract: We find an explicit Sn-equivariant bijection between the integral points in a certain zonotope in R, combinatorially equivalent to the permutahedron, and the set of m-parking functions of length n. This bijection restricts to a bijection between the regular Sn-orbits and (m,n)-Dyck paths, the number of which is given by the Fuss-Catalan number An(m, 1). Our motivation came from studying tilting bundles on noncommutative Hilbert schemes. As a side result we use these tilting bundles to construct a semi-orthogonal decomposition of the derived category of noncommutative Hilbert schemes.
1 citations
Peer Review•
25 Jul 2022
TL;DR: In this paper , a brief review of the cohomological Hall algebra CoHA H and the K-theoretical Hall algebra KHA R associated to quivers is given, and it is shown that there exists a homomorphism of algebras (obtained from a Chern character map) R → H ˜ σ where H is a Zhang twist of the completion of H .
Abstract: . We give a brief review of the cohomological Hall algebra CoHA H and the K-theoretical Hall algebra KHA R associated to quivers. In the case of symmetric quivers, we show that there exists a homomorphism of algebras (obtained from a Chern character map) R → ˆ H ˜ σ where ˆ H ˜ σ is a Zhang twist of the completion of H . Moreover, we establish the equivalence of categories of “locally finite” graded modules ˆ H ˜ σ - Mod lf ≃ R Q -Mod lf . Examples of locally finite ˆ H ˜ σ -, resp. R Q - modules appear naturally as the cohomology, resp. K-theory, of framed moduli spaces of quivers.