Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2

Bruce Allison; Stephen Berman; Arturo Pianzola

Displaying similar documents to “Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2”

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

Generalized Post algebras and their application to some infinitary many-valued logics

Cat-Ho Nguyen

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CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7 1. Definition and characterization of generalized Post algebras............................................. 7 2. Post...

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

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We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra $\hat{} (M)$ on the manifold M given in [gksv].

Metric generalizations of Banach algebras

W. Żelazko

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CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

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In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and $_{V} M$ is a good V-module.

Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{matrix} F_{m}^{1} \end{matrix}$ nilradical

L.M. Camacho, B.A. Omirov, K.K. Masutova, I.M. Rikhsiboev (2017)

Open Mathematics

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All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{matrix} F_{m}^{1} \end{matrix}$ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

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For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras $A_{p} (G, ω)$ . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We...

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

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A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{\infty}$ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

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We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where $A = ℓ^{p}$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras $ℓ^{p} (ω)$ .

Algorithmic computations of Lie algebras cohomologies

Šilhan, Josef

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From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package $L i E$ offers the data structures and corresponding procedures for...

On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

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Second duals of measure algebras

H. G. Dales, A. T.-M. Lau, D. Strauss

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Let G be a locally compact group. We shall study the Banach algebras which are the group algebra L¹(G) and the measure algebra M(G) on G, concentrating on their second dual algebras. As a preliminary we shall study the second dual C₀(Ω)” of the C*-algebra C₀(Ω) for a locally compact space Ω, recognizing this space as C(Ω̃), where Ω̃ is the hyper-Stonean envelope of Ω. We shall study the C*-algebra $B^{b} (Ω)$ of bounded Borel functions on Ω, and we shall determine the exact cardinality of a variety...

On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

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A new proof of the noncommutative Banach-Stone theorem

David Sherman (2006)

Banach Center Publications

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Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate...