Related papers: $S_n$-Equivariant Sheaves and Kozsul Cohomology

The Bitableax correspondence isomorphism/Koszul map Theorem (BCK Theorem, for short, Theorem 6.5 below) describes a relevant pair of mutually inverse vector space isomorphisms, the Koszul map K : U(gl(n))-> Sym(gl(n)) and the bitableaux…

Within the framework of braided or quasisymmetric monoidal categories braided Q-supersymmetry is investigated, where Q is a certain functorial isomorphism in a braided symmetric monoidal category. For an ordinary (co-)quasitriangular Hopf…

We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild…

We compare three definitions of the equivariant cohomological dimension of a group with operators, coming from Takasu, Adamson and Bredon relative group cohomologies, giving examples of strict inequality in all cases where it can occur. We…

In this paper we study a generalization of K\"ahler differentials, which correspond to the secondary Hochschild homology associated to a triple $(A,B,\varepsilon)$. We establish computations in low dimension, while also showing how this…

Let $B$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $B^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild…

For a projective hypersurface $Z$ with isolated singularities, we generalize some well-known assertions in the nonsingular case due to Griffiths, Scherk, Steenbrink, Varchenko, and others about the relations between the Steenbrink spectrum,…

Let $X$ a smooth quasi-projective algebraic surface, $L$ a line bundle on $X$. Let $X^{[n]}$ the Hilbert scheme of $n$ points on $X$ and $L^{[n]}$ the tautological bundle on $X^{[n]}$ naturally associated to the line bundle $L$ on $X$. We…

We discuss the Hochschild cohomology of the category of D-modules associated to an algebraic stack. In particular we describe the Hochschild cohomology of the category of torus-equivariant D-modules as the cohomology of a D-module on the…

The $K$-theory of a polynomial ring $R[t]$ contains the $K$-theory of $R$ as a summand. For $R$ commutative and containing $\Q$, we describe $K_*(R[t])/K_*(R)$ in terms of Hochschild homology and the cohomology of K\"ahler differentials for…

We compute the bi-Hamiltonian cohomology of an arbitrary dispersionless Poisson pencil in a single dependent variable using a spectral sequence method. As in the KdV case, we obtain that $BH^p_d(\hat{F}, d_1,d_2)$ is isomorphic to…

Nichols algebras are an important tool for the classification of Hopf algebras. Within those with finite GK dimension, we study homological invariants of the super Jordan plane, that is, the Nichols algebra $A=B(V(-1,2))$. These invariants…

We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's + construction are developed. In the special case of…

We propose an deepened analysis of KV-Poisson structures of on IR^2. We present their classification their properties an their possible applications in different domains. We prove that these structure give rise to a new Cohomological…

We show that certain semistable sheaves on the projective plane with linear Hilbert polynomial are cokernels of semistable morphisms of decomposable sheaves.We exhibit certain locally closed subvarieties of moduli spaces of semistable…

We prove analogues of the fundamental theorem of algebraic K-theory for the second and third homology of SL_2 over an infinite field k. The statements involve Milnor-Witt K-theory and scissors congruence groups. We use these results to…

We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic…

We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial $J(q)$, and the four-dimensional invariants are the Khovanov…

Applying recent results by Lowen-Van den Bergh we show that Hochschild cohomology is preserved under Koszul-Moore duality as a Gerstenhaber algebra. More precisely, the corresponding Hochschild complexes are linked by a quasi-isomorphism of…

We compute the Poisson cohomology associated with several three dimensional Lie algebras. Together with existing results and the classification of three dimensional Lie algebras, this provides the Poisson cohomology of all linear Poisson…