Related papers: Polarization Identities
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…
Three categories of algebras with morphisms generalising the usual set of algebra homomorphisms are described. The Sweedler product provides a hom-tensor equivalence relating these three categories, and a tool enabling the universal…
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
We introduce many new generalizations of Poisson algebras which can be constructed inside the associative algebra of linear transformations over a vector space.
We address a Jordan version of Johnson theorem on (associative) algebras of quotients, namely whether a strongly nonsingular (the Jordan version of nonsingularity) has a von Neumann regular algebra of quotients. Although the answer is…
A conjugation $C$ is an anti-linear isometric involution on a complex Hilbert space $\clh$, and $T\in \clb(\clh)$ is conjugate normal if $T^*T = CTT^*C$ holds for some conjugation (C). In this paper, we provide a factorization and range…
We present a geometric proof of the Poincar\'e-Dulac Normalization Theorem for analytic vector fields with singularities of Poincar\'e type. Our approach allows us to relate the size of the convergence domain of the linearizing…
Let $k$ be an algebraically closed base field of characteristic zero. The category equivalence between central simple algebras and irreducible, generically free $PGL_n$-varieties is extended to the context of central simple algebras with…
We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We…
The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…
Motivated by the study of H\"ormander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as…
We consider associative algebras with involution graded by a finite abelian group G over a field of characteristic zero. Suppose that the involution is compatible with the grading. We represent conditions permitting PI-representability of…
This paper aims at studying how finitely many generalized polarization tensors of an algebraic domain can be used to determine its shape. Precisely, given a planar set with real algebraic boundary, it is shown that the minimal polynomial…
We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces.
A higher dimensional generalization of the cross product is associated with an adequate matrix multiplication. This index-free view allows for a better understanding of the underlying algebraic structures, among which are generalizations of…
If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an…