Related papers: AC-KBO Revisited

We investigate properties of varieties of algebras described by a novel concept of equation that we call \emph{commutator equation}. A commutator equation is a relaxation of the standard term equality obtained substituting the equality…

We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…

In this paper we generalize the axiom systems given by M. Pa{\l}asi\'nski, B. Wo\'zniakowska and by W.H. Cornish for commutative BCK-algebras to the case of commutative pseudo BCK-algebras. A characterization of commutative pseudo…

We consider an abstract Wick ordering as a family of relations on elements a_i and define *-algebras by these relations. The relations are given by a fixed operator T:h\otimes h --> h \otimes h, where h is one-particle space, and they…

Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…

An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…

Sufficient conditions on a space are given which guarantee that the $K$-theory ring and the ordinary cohomology ring with coefficients over a principal ideal domain are invariants of, respectively, the adic genus and the SNT set. An…

Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…

The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…

Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild…

Let $K$ be a positive compact operator on a Banach lattice. We prove that if either $[K>$ or $<K]$ is ideal irreducible then $[K>=<K]=L_+(X)\cap {K}'$. We also establish the Perron-Frobenius Theorem for such operators $K$. Finally we apply…

This survey article on bivariant Kasparov theory and E-theory is mainly intended for readers with a background in homotopical algebra and category theory. We approach both bivariant K-theories via their universal properties and equip them…

Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…

We consider a recursive scheme for defining the coefficients in the operator product expansion (OPE) of an arbitrary number of composite operators in the context of perturbative, Euclidean quantum field theory in four dimensions. Our…

We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions to normal forms, and employ them to construct cubical…

A categorical axiomatic theory of creation/annihilation operators on bosonic Fock space is introduced and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.

The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a…

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…

It is a theorem of Ribet that an abelian variety defined over a number field $K$ has only finitely many torsion points with values in the maximal cyclotomic extension field $K^{\mathrm{cyc}}$ of $K$. Recently, R\"ossler and Szamuely…

We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action…