Related papers: Algebras with non-periodic bounded modules
We find a new braided Hopf structure for the algebra satisfied by the entries of the braided matrix $BSL_q(2)$. A new nonbraided algebra whose coalgebra structure is the same as the braided one is found to be a two parameter deformed…
We say that an algebra A is periodic if it has a periodic projective resolution as an (A,A)-bimodule. We show that any self-injective algebra of finite representation type is periodic. To prove this, we first apply the theory of smash…
Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…
Nonassociative algebras satisfying the polynomial identities x(yz)=y(xz) and (xy)z=(xz)y are called bicommutative. We prove the following results: (i) Finitely generated bicommutative algebras are weakly noetherian, i.e., satisfy the…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
We observe that for a large class of non-amenable groups $G$, one can find bounded representations of $A(G)$ on Hilbert space which are not completely bounded. We also consider restriction algebras obtained from $A(G)$, equipped with the…
In this note we extend the spectral theorem for bimodules to the higher rank graph C*-algebra context. Under the assumption that the graph is row finite and has no sources, we show that a bimodule over a natural abelian subalgebra is…
We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding…
We study the complexity of multiplication in noncommutative group algebras which is closely related to the complexity of matrix multiplication. We characterize such semisimple group algebras of the minimal bilinear complexity and show…
We examine when division algebras can share common splitting fields of certain types. In particular, we show that one can find fields for which one has infinitely many Brauer classes of the same index and period at least 3, all…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
A representation theory for Bol algebras is proposed. For a suitable (2,3)-cohomology theory for Bol algebras, we define a (2,3)-coboundary with companion and next we define a (2,3)-cohomology group. Deformations of Bol algebras are…
The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie algebras $L=\sum_{i\in \mathbb Z}L_i,$ over an algebraically closed field of characteristic…
Let $k$ be a field of odd prime characteristic $p$. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over $k$. As a consequence, we prove that if $B$ is a defect…
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…
We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…