Related papers: The van Est spectral sequence for Hopf algebras
The correspondence between Lie algebras, Lie groups, and algebraic groups, on one side and commutative Hopf algebras on the other side are known for a long time by works of Hochschild-Mostow and others. We extend this correspondence by…
To any Hopf algebra H we associate two commutative Hopf algebras, which we call the first and second lazy homology Hopf algebras of H. These algebras are related to the lazy cohomology groups based on the so-called lazy cocycles of H by…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
We obtain a decomposition for the Hochschild cochain complex of a split algebra and we study some properties of the cohomology of each term of this decomposition. Then, we consider the case of trivial extensions, specially of Frobenius…
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal…
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
We show that the theory of Lie algebra cohomology can be recast in a topological setting and that classical results, such as the Shapiro lemma and the van Est isomorphism, carry over to this augmented context.
We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information,…
Following ideas of Graeme Segal, we construct an equivariant con- figuration space that is a model of equivariant connective K-homology spec- trum for finite groups, as a consequence we obtain an induction structure for equivariant…
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Then, we define a Hom-exponential (Hexp) map from the Hom-Lie…
We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. As an application, we describe the BRST reduction of the chiral Hecke algebra as a vertex super algebra.
We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf…
The aim of this paper is to introduce the notion of restricted Hom- Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to…
For complex parallelisable manifolds $\Gamma\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Fr\"olicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure…
A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the…
We prove a series of van Est type theorems relating the cohomologies of strict Lie 2-groups and strict Lie 2-algebras and use them to prove the integrability of Lie 2-algebras anew.
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
Operadic tangent cohomology generalizes the existing cohomology theories of Chevalley--Eilenberg, Hochschild, and Harrison to address the deformation theory of general types of algebras through gadgets known as deformation complexes. The…
We study a spectral sequence approximating Lie algebroid cohomology associated to a Lie subalgebroid. This is a simultaneous generalisation of several classical constructions in differential geometry, including the Leray-Serre spectral…
In this paper we establish a connection between the cohomology of a modular Lie algebra and its p-envelopes. We also compute the cohomology of Zassenhaus algebras and their minimal p-envelopes with coefficients in generalized baby Verma…