Related papers: Semi-derived Ringel-Hall bialgebras

We revisit a class of examples described in the original paper on biproducts, expand the class, and provide a detailed analysis of the coalgebra and algebra structures of many of these examples. Connections with the semisimple Hopf algebras…

We say that a Hopf algebra H is semicocommutative if the right adjoint coaction factorizes through the tensor product of H with the center of H. For instance the commutative and the cocommutative Hopf algebras are semicocommutative. The…

We construct a Hopf algebra cocycle in the Yangian double $DY(SL_{2})$, conjugating Drinfeld's coproduct to the usual one. To do that, we factorize the twist between two ``opposite'' versions of Drinfeld's coproduct, introduced in earlier…

In this report we give an intrinsic treatment of the results we developed in a previous work connecting the differential calculi on Hopf algebras to the Drinfeld double. In the first place we recover that bicovariant bimodules are in one to…

In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…

For a maximal separable subfield $K$ of a central simple algebra $A$, we provide a semiring isomorphism between $K$-$K$-bimodules $A$ and $H$-$H$ bisets of $G = \Gal(L/F)$, where $F = \operatorname{Z}(A)$, $L$ is the Galois closure of…

For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The family is parameterized by partitions of the quiver into Dynkin subquivers. For each such partition, we write the domain…

The ${\ell}^1$-convolution algebra of a semilattice is known to have trivial cohom ology in degrees 1,2 and 3 whenever the coefficient bimodule is symmetric. We ex tend this result to all cohomology groups of degree $\geq 1$ with symmetric…

Let A and B be two connected graded commutative k-algebras of finite type, where k is a perfect field of positive characteristic p. We prove that the quasi--shuffle algebras generated by A and B are isomorphic as Hopf algebras if and only…

The origin and interplay of products and dualities in algebraic (co)homology theories is ascribed to a $\times_A$-Hopf algebra structure on the relevant universal enveloping algebra. This provides a unified treatment for example of results…

In this paper we point out the natural relation between $\mathbb Q$-twisted objects of the derived category of abelian varieties, cohomological rank functions, and semihomogeneous vector bundles. We apply this to two basic classes of…

We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all…

We extend our work in~\cite{rm01} to the case of Hopf comodule coalgebras. We introduce the cocylindrical module $C \natural^{} \mathcal{H}$, where $\mathcal{H}$ is a Hopf algebra with bijective antipode and $C$ is a Hopf comodule coalgebra…

Let A a k-algebra, H a Hopf algebra, E = A#H a general crossed product and M an E-bimodule. We obtain a complex simpler than the canonical one, giving the Hochschild homology of E with coefficients in M. This complex is eqquiped with a…

We show that for dually paired bialgebras, every comodule algebra over one of the paired bialgebras gives a comodule algebra over their Drinfeld double via a crossed product construction. These constructions generalize to working with…

We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. We also describe by quivers with relations all algebras derived equivalent to a quasi-hereditary algebra with two…

We introduce the Hom-analogue of the L-R-smash product and use it to define the Hom-analogue of the diagonal crossed product. When H is a finite dimensional Hom-Hopf algebra with bijective antipode and bijective structure map, we define the…

When $\mathfrak h$ is a toral subalgebra of a Lie algebra $\mathfrak g$ over a field $\mathbf k$, and $M$ a $\mathfrak g$-module on which $\mathfrak h$ also acts torally, the Hochschild-Serre filtration of the Chevalley-Eilenberg cochain…

A Laurent polynomial ring $A[t,1/t]$ with coefficients in a unital ring $A$ determines a category of quasi-coherent sheaves on the projective line over $A$; its $K$-theory is known to split into a direct sum of two copies of the $K$-theory…

Consider the Cohomological Hall Algebra as defined by Kontsevich and Soibelman, associated with a Dynkin quiver. We reinterpret the geometry behind the multiplication map in the COHA, and give an iterated residue formula for it. We show…