Related papers: On the Structure of the Fusion Ideal

We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n…

We classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.

We generalize certain parts of the theory of group rings to the twisted case. Let G be a finite group acting (possibly trivially) on a field L of characteristic coprime to the order of the kernel of this operation. Let K in L be the fixed…

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute the generic fusion rules of the Grothendieck ring of Rep(PSL(2,q)), q prime-power, by applying a Verlinde-like formula on the…

The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the…

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…

For a saturated fusion system $\mathcal F$ on a $p$-group $S$, we study the Burnside ring of the fusion system $B(\mathcal F)$, as defined by Matthew Gelvin and Sune Reeh, which is a subring of the Burnside ring $B(S)$. We give criteria for…

Let G be a connected reductive group and G/H a spherical homogeneous space. We show that the ideal of relations between a natural set of generators of the Cox ring of a G-embedding of G/H can be obtained by homogenizing certain equations…

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…

Let $B$ be a finite CW complex and $G$ a compact connected Lie group. We show that the number of gauge groups of principal $G$-bundles over $B$ is finite up to $A_n$-equivalence for $n<\infty$. As an example, we give a lower bound of the…

We study the fusion semirings arising from easy quantum groups. We classify all the possible free ones, answering a question of T. Banica and R. Vergnioux : these are exactly the fusion rings of quantum groups without any nontrivial…

The generalized order $e_G(g)$ of an element $g$ of a group $G$ is the smallest positive integer $k$ such that there exist $x_1,\ldots,x_k \in G$ such that $g^{x_1} \ldots g^{x_k}=1$, where $g^x=x^{-1}gx$. Let $e(G) = \max \{e_G(g)\ |\ g…

Let O be the ring of S-integers in a number field k. We prove that if the group of units O^* is infinite then every matrix in $\Gamma$ = SL_2(O) is a product of at most 9 elementary matrices. This completes a long line of research in this…

For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over…

We find necessary and sufficient conditions for the finite separability of monogenic rings. As a corollary, we prove that a finitely generated torsion-free PI-ring is finitely separable if and only if its additive group is finitely…

For any finite type connected surface $S$, we give an infinite presentation of the fundamental group $\pi_1(S,\ast)$ of $S$ based at an interior point $\ast\in{S}$ whose generators are represented by simple loops. When $S$ is…

We study the problem of determining if the braid group representations obtained from quantum groups of types $E, F$ and $G$ at roots of unity have infinite image or not. In particular we show that when the fusion categories associated with…

We express the discriminant of the polynomial relations of the fusion ring, in any conformal field theory, as the product of the rows of the modular matrix to the power -2. The discriminant is shown to be an integer, always, which is a…

In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known…