Related papers: Some notes on the ternary modular commutator
The aim of this note is: (a) to propose a generalization of tetrahedron equations from \cite{S} and of their solutions. Due to appearance of a larger number of parameters the $R$-matrices from \cite{S} will be replaced by…
We will use Watts's theorem together with Lenzing's characterization of finitely presented modules via commuting properties of the induced tensor functor in order to study commuting properties of Ext-covariant functors.
In this paper, we study the combinatorics of congruence subgroups of the modular group by generalizing results obtained in the non-modular case. For this, we define a notion of irreducible solutions from which we can build all the…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
In this paper we follow the constructions of Turaev's book [Tu] closely, but with small modifications, to construct of a modular functor, in the sense of Kevin Walker, from any modular tensor category. We further show that this modular…
We outline the construction of differential invariants for higher--rank tensors.
We investigate the interaction between the product of invariant types and domination-equivalence. We present a theory where the latter is not a congruence with respect to the former, provide sufficient conditions for it to be, and study the…
The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the variety COM of all commutative semigroups or…
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…
In the paper, we generalize some congruences of Lehmer for general composite numbers.
The purpose of this article is to investigate triangularization and simultaneous triangularization of matrices over max algebras using graph theoretic methods. We establish a connection between commutators and commutants with simultaneous…
We examine the modular properties of nonrenormalizable superpotential terms in string theory and show that the requirement of modular invariance necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In a class of…
The goal of this article is to construct and study connective versions of topological modular forms of higher level like $\mathrm{tmf}_1(n)$. In particular, we use them to realize Hirzebruch's level-$n$ genus as a map of ring spectra.
We propose the ternary generalization of the classical anti-commutativity and study the algebras whose generators are ternary anti-commutative. The integral over an algebra with an arbitrary number of generators N is defined and the formula…
We discuss the problem to develop a mathematical theory of a certain class of nonrational conformal field theories (CFT) which contain the unitary CFT. A variant of the concept of a modular functor is proposed that appears to be suitable…
We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.
We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.
In this paper, we shall find a new connection between $n$th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discuss the recent work been done in sequences and their…
This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…
Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very…