Search results for "LYN"
showing 10 items of 910 documents
Identities of *-superalgebras and almost polynomial growth
2015
We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces
2007
We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak ∗ separable admits a closed linear subspace whose dual is not weak ∗ -separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2homogeneous polynomials.
On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials
2007
Given an operator ideal I, we study the multi-ideal I ο L and the polynomial ideal I ο P). The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained.
Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions
2002
Our main result shows that every Montel Kothe echelon or coechelon space E of order 1 < p ≤ ∞ is nuclear if and only if for every (some) m ≥ 2 the space ((mE), τ0) of m-homegeneus polynomials on E endowed with the compact-open topology τ0 has an unconditional basis if and only if the space (ℋ(E), τδ) of holomorphic functions on E endowed with the bornological topology τδ associated to τ0 has an unconditional basis (for coechelon spaces τδ equals τ0). The main idea is to extend the concept of the Gordon-Lewis property from Banach to Frechet and (DF) spaces. In this way we obtain techniques which are used to characterize the existence of unconditional basis in spaces of m-th (symmetric) tenso…
Polynomial Identities and Asymptotic Methods
2005
Polynomial identities and PI-algebras $S_n$-representations Group gradings and group actions Codimension and colength growth Matrix invariants and central polynomials The PI-exponent of an algebra Polynomial growth and low PI-exponent Classifying minimal varieties Computing the exponent of a polynomial $G$-identities and $G\wr S_n$-action Superalgebras, *-algebras and codimension growth Lie algebras and nonassociative algebras The generalized-six-square theorem Bibliography Index.
The Herzog-Vasconcelos conjecture for affine semigroup rings
1999
Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.
Polynomial growth of the codimensions: a characterization
2009
Let A A be a not necessarily associative algebra over a field of characteristic zero. Here we characterize the T-ideal of identities of A A in case the corresponding sequence of codimensions is polynomially bounded.
The maximal coefficient of ternary cyclotomic polynomials with one free prime
2014
A cyclotomic polynomial Φn(x) is said to be ternary if n = pqr, with p, q and r distinct odd primes. Let M(p, q) be the maximum (in absolute value) coefficient appearing in the polynomial family Φpqr(x) with p < q < r, p and q fixed. Here a stronger version of the main conjecture of Gallot, Moree and Wilms regarding M(p, q) is established. Furthermore it is shown that there is an algorithm to compute M(p): = max {M(p, q): q > p}. Our methods are the most geometric used so far in the study of ternary cyclotomic polynomials.
On a representation theorem for finitely exchangeable random vectors
2016
A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$. We give an alternative and shorter proof of the representation result (Jaynes \cite{Jay86} and Kerns and Sz\'ekely \cite{KS06}) stating that the law of $X$ is a mixture of product probability measures with respect to a signed mixing measure. The result is "finitistic" in nature meaning that it is a matter of linear algebra for finite $S$. The passing from finite $S$ to an arbitrary one may pose some measure-theoretic difficulties which are avoided by our p…
On almost nilpotent varieties of subexponential growth
2015
Abstract Let N 2 be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity x ( y z ) ≡ 0 . We introduce two new varieties, denoted by V sym and V alt , contained in the variety N 2 and we prove that V sym and V alt are the only two varieties almost nilpotent of subexponential growth.