Related papers: Trace Forms of Symbol Algebras
Our motivating question was whether all traces on a U-ultrapower of a C*-algebra A, where U is a non-principal ultrafilter on N, are necessarily U-limits of traces on A. We show that this is false so long as A has infinitely many extremal…
An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…
The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…
Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…
We characterize the signature of piecewise continuously differentiable paths transformed by a polynomial map in terms of the signature of the original path. For this aim, we define recursively an algebra homomorphism between two shuffle…
To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth…
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some…
The classical number system encodes magnitude using a single scalar value whose sign positive or negative has remained conceptually unchanged for centuries. This work introduces Multisign Algebra, a mathematical generalization of the sign…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
Traces form a coarse notion of semantic equivalence between states of a process, and have been studied coalgebraically for various types of system. We instantiate the finitary coalgebraic trace semantics framework of Hasuo et al. for…
Semialgebraic splines are functions that are piecewise polynomial with respect to a cell decomposition into sets defined by polynomial inequalities. We study bivariate semialgebraic splines, formulating spaces of semialgebraic splines in…
Motivated by recent advances in Catalan combinatorics, we study special values of the standard trace on affine Hecke algebras. Starting from a generating function for this trace calculated by Opdam, we use the theory of Szenes and Vergne to…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
We show that a structural matrix algebra $A$ is isomorphic to the endomorphism algebra of an algebraic-combinatorial object called a generalized flag. If the flag is equipped with a group grading, an algebra grading is induced on $A$. We…
We show here how residue calculus (residue currents, Grothendieck residues, duality theorem) can be used to obtain an algebraic characterization of the Abel-transform of a meromorphic form on germs of analytic sets. We prove by this way a…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Symplectic reflection algebra $ H_{1, \,\nu}(G)$ has a $T(G)$-dimensional space of traces whereas, when considered as a superalgebra with a natural parity, it has an $S(G)$-dimensional space of supertraces. The values of $T(G)$ and $S(G)$…
In this paper we introduce the notion of twisted symplectic reflection algebras and describe the category of representations of such an algebra associated to a non-faithful G-action in terms of those for faithful actions of G.
Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test…
Every finite-dimensional representation of an algebraic group G gives a trace symmetric bilinear form on the Lie algebra of G. We give criteria in terms of root system data for the existence of a representation such that this form is…