Related papers: Multihomogeneous Normed Algebras and Polynomial Id…

In this article, we study the multiparameter second quantum Weyl algebra at roots of unity. In this setting, the algebra is a polynomial identity (PI) algebra, and the dimension of its simple modules is bounded above by its PI degree. We…

For a tuple $A=(A_0, A_1, ..., A_n)$ of elements in a unital Banach algebra ${\mathcal B}$, its {\em projective spectrum} $p(A)$ is defined to be the collection of $z=[z_0, z_1, ..., z_n]\in \pn$ such that $A(z)=z_0A_0+z_1A_1+... +z_nA_n$…

The aim of this paper is to prove a stronger version of a conjecture on the existence of non-dominated scalar-valued m-homogeneous polynomials (m>=3) on arbitrary infinite dimensional Banach spaces.

A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We…

Let ${\mathcal A}$ and ${\frak A}$ be Banach algebras such that ${\mathcal A}$ is a Banach ${\frak A}$-bimodule with compatible actions. We define the product ${\cal A}\rtimes{\frak A}$, which is a strongly splitting Banach algebra…

We study polynomial identities of nonassociative algebras constructed by using infinite binary words and their combinatorial properties. Infinite periodic and Sturmian words were first applied for constructing examples of algebras with…

We prove that subhomogeneous continuous Banach bundles over compact metrizable spaces are equivalent to Hilbert bundles, while examples show that the metrizability assumption cannot be dropped completely. This complements the parallel…

The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…

We consider associative algebras over a field. An algebra variety is said to be {\em Lie nilpotent} if it satisfies a polynomial identity of the kind $[x_1, x_2, ..., x_n] = 0$ where $[x_1,x_2] = x_1x_2 - x_2x_1$ and $[x_1, x_2, ..., x_n]$…

To every Gorenstein algebra $A$ of finite vector space dimension greater than 1 over a field $\FF$ of characteristic zero, and a linear projection $\pi$ on its maximal ideal ${\mathfrak m}$ with range equal to the annihilator…

Let $L$ and $H$ be finite-dimensional restricted Lie algebras over a perfect field $\F$ such that $u(L)\cong u(H)$, where $u(L)$ is the restricted enveloping algebra of $L$. We prove that if $L$ is $p$-nilpotent and abelian, then $L\cong…

This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if $B$ is a unital commutative semisimple Banach algebra with…

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasinorms instead of norms. In this paper we develop a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the…

We prove that no separable Banach algebra is universal for homomorphic embeddings of all separable Banach algebras, whether embeddings are merely bounded or required to be contractive. The same holds in the commutative category. The proof…

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…

A 2-step nilpotent Lie algebra n is called nonsingular if ad(X): n --> [n,n] is onto for any X not in [n,n]. We explore nonsingular algebras in several directions, including the classification problem (isomorphism invariants), the existence…

We state criteria for a nilpotent Lie algebra $\g$ to admit an invariant metric. We use that $\g$ possesses two canonical abelian ideals $\ide(\g) \subset \mathfrak{J}(\g)$ to decompose the underlying vector space of $\g$ and then we state…

In this paper we address the following question: is it always possible to choose a deformation quantization of a Poisson algebra A so that certain Poisson-commutative subalgebra C in it remains commutative? We define a series of…

Polyadic arithmetics is a branch of mathematics related to $p$--adic theory. The aim of the present paper is to show that there are very close relations between polyadic arithmetics and the classic theory of commutative Banach algebras.…

In this paper, we systematically investigate the nilpotentizer and nilpotent graph for a Lie superalgebra over the field of characteristic not equal to 2. First, we establish some fundamental properties of the nilpotentizer. Next, we show…