Related papers: Classification of pseudo $H$-type algebras
Let $q$ be a prime number, $k$ an algebraically closed field of characteristic 0, and $H$ a non-trivial semisimple Hopf algebra of dimension $2q^3$. This paper proves that $H$ can be constructed either from group algebras and their duals by…
With any non necessarily orientable unpunctured marked surface (S,M) we associate a commutative algebra, called quasi-cluster algebra, equipped with a distinguished set of generators, called quasi-cluster variables, in bijection with the…
Masuoka proved (2009) that a finite-dimensional irreducible Hopf algebra $H$ in positive characteristic is semisimple if and only if it is commutative semisimple if and only if the Hopf subalgebra generated by all primitives is semisimple.…
In this paper we will be classifying some regular upper-triangular subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to conjugacy by matrices in $SL(n, \mathbb C)$. We do so for dimension 2, codimension 1, and codimension 2 subalgebras. We…
We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$, we explicitly determine the algebra structure up to isomorphism for the link…
We try to classify Hopf algebras with the Chevalley property according to their derived representation type. We show that a finite-dimensional indecomposable non-semisimple Hopf algebra $H$ with the Chevalley property is derived discrete if…
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_{n,3} which contains the previously studied filiform nilpotent algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it turns out that…
Let $(H,R)$ be a quasitriangular weak Hopf algebra over a field $k$. We show that there is a braided monoidal equivalence between the Yetter-Drinfeld module category $^H_H\mathscr{YD}$ over $H$ and the category of comodules over some…
We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish…
Let $(\mathfrak{g},\tau)$ be a real simple symmetric Lie algebra and let $W \subset \mathfrak{g}$ be an invariant closed convex cone which is pointed and generating with $\tau(W) = -W$. For elements $h \in \mathfrak{g}$ with $\tau(h) = h$,…
We show that an arbitrary algebra ${ A}$, (of arbitrary dimension, over an arbitrary base field and any identity is not suppose for the product), is semisimple if and only if it has zero annihilator and admits a semi-division linear basis.…
Associated to every complex reflection group, we construct a lattice of quotients of its braid monoid-algebra, which we term nil-Hecke algebras, and which are obtained by killing all braid words that are "sufficiently long", as well as some…
We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…
The abelian category of tetramodules over an associative bialgebra $A$ is related with the Gerstenhaber-Schack (GS) cohomology as $Ext_\Tetra(A,A)=H_\GS(A)$. We construct a 2-fold monoidal structure on the category of tetramodules of a…
We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…
In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\mathbb{Z}^+$-graded Lie conformal algebras…
We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant…
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…
To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with…
We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to semisimple orbits, have infinite dimension. We introduce a new criterium to determine when a…