Related papers: On real algebras generated by positive and nonnega…
We prove the following. Let $R$ be a Noetherian ring, $B$ a finitely generated $R$-algebra, and $A$ a pure $R$-subalgebra of $B$. Then $A$ is finitely generated over $R$.
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
In this paper, we characterize the C*-Algebra generated by partial isometries.
As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevisky \cite{[4]}, in this paper, we give the test method of positive…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
Let K be a field of any characteristic and let R be an algebra generated by two elements satisfying quadratic equations. Then R is a homomorphic image of F=K<x,y | x^2+ax+b=0,y^2+cy+d=0> for suitable a,b,c,d in K. We establish that F can be…
Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…
The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
Associative or Jordan algebras generated by two idempotents are described precisely.
Given a finite-dimensional noncommutative semisimple algebra $A$ with involution, we show that $A$ always has an RBA-basis. We look for an RBA-basis that has integral or rational structure constants, and ask if the RBA admits a positive…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…
In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…
We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…