Search results for "Algebras"
showing 10 items of 281 documents
Lie Algebras Generated by Extremal Elements
1999
We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.
Structure of locally convex quasi C * -algebras
2008
There are examples of C*-algebras A that accept a locally convex *-topology τ coarser than the given one, such that Ã[τ] (the completion of A with respect to τ) is a GB*-algebra. The multiplication of A[τ] may be or not be jointly continuous. In the second case, Ã[*] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ã[τ] are investigated. If Ã+ τ denotes the τ-closure of the positive cone A+ of the given C*-algebra A, then the property Ā+ τ ∩ (-Ā+ τ) = {0} is decisive for the existence of certain faithful *-representations of the corresponding *-algebra Ã[τ]
Modernās elementārās algebras un ģeometrijas elementi matemātikas skolotājiem
2020
Grāmata paredzēta studiju kursa “Modernās elementārās algebras un ģeometrijas elementi” (4 kredītpunkti) apguvei integrētās profesionālās bakalaura studiju programmas “Skolotājs” studentiem. Tajā iekļauts teorijas materiāls, uzdevumu piemēri un uzdevumi ar atrisinājumiem patstāvīgajam darbam. Materiālu var izmantot arī matemātikas skolotāji mācību procesā, gatavojot vidusskolēnus matemātikas olimpiādēm.
Characters, bilinear forms and solvable groups
2016
Abstract We prove a number of results about the ordinary and Brauer characters of finite solvable groups in characteristic 2, by defining and using the concept of the extended nucleus of a real irreducible character. In particular we show that the Isaacs canonical lift of a real irreducible Brauer character has Frobenius–Schur indicator +1. We also show that the principal indecomposable module corresponding to a real irreducible Brauer character affords a quadratic geometry if and only if each extended nucleus is a split extension of a nucleus.
Obstruction theory in action accessible categories
2013
Abstract We show that, in semi-abelian action accessible categories (such as the categories of groups, Lie algebras, rings, associative algebras and Poisson algebras), the obstruction to the existence of extensions is classified by the second cohomology group in the sense of Bourn. Moreover, we describe explicitly the obstruction to the existence of extensions in the case of Leibniz algebras, comparing Bourn cohomology with Loday–Pirashvili cohomology of Leibniz algebras.
A note on cocharacter sequence of Jordan upper triangular matrix algebra
2016
Let UJn(F) be the Jordan algebra of n × n upper triangular matrices over a field F of characteristic zero. This paper is devoted to the study of polynomial identities satisfied by UJ2(F) and UJ3(F). In particular, the goal is twofold. On one hand, we complete the description of G-graded polynomial identities of UJ2(F), where G is a finite abelian group. On the other hand, we compute the Gelfand–Kirillov dimension of the relatively free algebra of UJ2(F) and we give a bound for the Gelfand–Kirillov dimension of the relatively free algebra of UJ3(F).
Relative principal congruences in congruence-modular quasivarieties
1998
The problem of definability of relative principal congruences in relatively congruence modular (RCM) quasivarieties is investigated. The RCM quasivarieties are characterized in terms of parameterized families of finite sets of pairs of terms which define relative principal congruences.
The diamond partial order for strong Rickart rings
2016
The diamond partial order has been first introduced for matrices, and then discussed also in the general context of *-regular rings. We extend this notion to Rickart rings, and state various properties of the diamond order living on the so-called strong Rickart rings. In particular, it is compared with the weak space preorder and the star order; also existence of certain meets and joins under diamond order is discussed.
Extensions of hermitian linear functionals
2022
AbstractWe study, from a quite general point of view, the family of all extensions of a positive hermitian linear functional $$\omega $$ ω , defined on a dense *-subalgebra $${\mathfrak {A}}_0$$ A 0 of a topological *-algebra $${\mathfrak {A}}[\tau ]$$ A [ τ ] , with the aim of finding extensions that behave regularly. The sole constraint the extensions we are dealing with are required to satisfy is that their domain is a subspace of $$\overline{G(\omega )}$$ G ( ω ) ¯ , the closure of the graph of $$\omega $$ ω (these are the so-called slight extensions). The main results are two. The first is having characterized those elements of $${\mathfrak {A}}$$ A for which we can find a positive her…
Algebras of unbounded operators and physical applications: a survey
2009
After a historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance in physical applications.