101.
C-Star-Algebra -- from MathWorld
- Weisstein, Eric W.
A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies (x^*)^* = x x^*y^* = (yx)^* x^*+y^* = (x+y)^* (cx)^* = \bar cx^*, where \bar c is the complex conjugate of c, and whose norm satisfies \left\Vert{xx^*}\right\Vert=\left\Vert{x}\right\Vert^2. See also: K-Theory, Pre-C-Star-Algebra
102.
Lattice valued algebras.
- Nola, Antonio di; Gerla, Giangiacomo
In this paper we propose a general approach to the theory of fuzzy algebras, while the early existing papers deal with a particular type of fuzzy structures as fuzzy groups, fuzzy ideals, fuzzy vector spaces and so on.
103.
Nonassociative ultraprime normed algebras
- Rodríguez Palacios, Angel; Cabrera García, M.
Recently M. Mathieu [9] has proved that any associative ultraprime normed complex algebra is centrally closed. The aim of this note is to announce the general nonassociative extension of Mathieu's result obtained by the authors [2].
104.
Identidades graduadas para algebras de matrizes
- Sergio Sardinha de Azevedo
The study of graded polynomial identities was motivated by its many applications to Polynomial Identities Theory, like the structure theory developed by A. Kemer. Afterwards it has become an independent object of study. The graded identities can give us interesting information about the ordinary identities. At first working with matrices of order n over infinite fields, we have found bases for the graded identities of this algebra considering Zn-grading and Z-grading. We have also proved that, up to isomorphism, there exist two non-trivial Z2-gradings for the algebra of the matrices 2×2 over a finite field of characteristic different from 2....
105.
Alternative Algebra -- from MathWorld
- Weisstein, Eric W.
Let A denote an \mathbb{R}-algebra, so that A is a vector space over R and A\times A\to A (x,y)\mapsto x\cdot y. Then A is said to be alternative if, for all x,y\in A, (x\cdot y)\cdot y=x\cdot(y\cdot y) (x\cdot x)\cdot y=x\cdot(x\cdot y). Here, vector multiplication x\cdot y is assumed to be bilinear. The associator (x,y,z) is an alternating function, and the subalgebra generated by two elements is associative. See also: Associator
106.
Kit Algebras
- Thomas Br Ustle
One of the main tools in representation theory of finite-dimensional
algebras is the one-point extension technique. It allows to determine
the representation type of an algebra whose quiver is obtained by
iterated addition of sinks or sources. For large algebras, however, it
seems more appropriate to glue together several parts at once. We
introduce such a technique here. The resulting algebras are called kit
algebras. We present a criterion when a kit algebra is tame.
In this paper we introduce a method to construct certain tame algebras
by "glueing" smaller algebras together. These are called "kit algebras". This
method extends the well-known one-point extension technique and uses essentially
the Gelfand-type...
107.
Generalizations of Jordan Algebras and Malcev Algebras
- Liu, Keqin
We introduce two classes of nonassociative algebras and define the building
blocks in the context of the new nonassociative algebras.
108.
Symmetrization of Brace Algebras
- Daily, Marilyn; Lada, Tom
We show that the symmetrization of a brace algebra structure yields the
structure of a symmetric brace algebra.
109.
The Stable Rank Of Tensor Products Of Free Product C*-Algebras
- Kenneth J. Dykema; Algebras A
. Let A be the minimal tensor product of C --algebras, A (j) , which are reduced free products with respect to traces of C --algebras that are not too small in a specific sense. Then the stable rank of A is 1. Introduction. The (topological) stable rank, sr(A), of a Banach algebra, A, was invented by Rieffel [4] and is intimately related to "non--stable" K--theory. The case sr(A) = 1 has been of particular interest; by definition, sr(A) = 1 if and only if the invertible elements of A are dense in A. Recently, Villadsen [6] constructed the first...
110.
Steenrod Algebra -- from MathWorld
- Weisstein, Eric W.
The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every n \in \mathbb{Z} and i \in \{0, 1, 2, 3, \dots\} there are natural transformations of functors Sq^i: H^n(\bullet;\mathbb{Z}_{2}) \to H^{n+i}(\bullet;\mathbb{Z}_{2}) satisfying: 1. Sq^i = 0 for i > n. 2. Sq^n(x) = x\smile x for all x\in H^n(X,A;\mathbb{Z}_{2}) and all pairs (X, A). 3. Sq^0 = id_{H^n(\bullet;\mathbb{Z}_{2})}. 4. The Sq^i maps commute with the...
111.
Isometries between C*-algebras
- Chu, Cho-Ho; Wong, Ngai-Ching
Let $A$ and $B$ be C*-algebras and let $T$ be a linear isometry
from $A$ \emph{into} $B$. We show that there is a largest
projection $p$ in $B^{**}$ such that $T(\cdot)p : A
\longrightarrow B^{**}$ is a Jordan triple homomorphism and
$$
T(a b^* c + c b^* a) p= T(a) T(b)^* T(c) p + T(c) T(b)^* T(a) p
$$
for all $a$, $b$, $c$ in $A$. When $A$ is abelian, we have
$\|T(a)p\|=\|a\|$ for all $a$ in $A$. It follows that a (possibly
non-surjective) linear isometry between any C*-algebras reduces
{\it locally} to a Jordan triple isomorphism, by a projection.
112.
Power Associative Algebra -- from MathWorld
- Weisstein, Eric W.
An algebra in which the associator (x,x,x) = 0. The subalgebra generated by one element is associative. See also: Associator
113.
PI equivalencia e não equivalencia de algebras
- Sergio Mota Alves
As álgebras verbalmente primas são bem conhecidas em característica 0, já sobre corpos de característica p >2 pouco sabemos sobre elas. Nesse trabalho vamos discutir algumas diferenças entre estes dois casos de característica sobre corpos infinitos. Iniciamos mostrando que o Teorema do Produto Tensorial de Kemer e duas de suas conseqüências não podem ser transportados para corpos infinitos de característica positiva p >2. Em seguida, discutiremos algumas propriedades envolvendo as álgebras Aa;b, a saber, mostraremos que as álgebras Aa;b e Ma+b(E) não são PI-equivalentes e que as álgebras Aa;a e Ma;a (E) não são PI-equivalentes, e apresentaremos um resultado...
114.
Caracterisations de certain algebres de Banach par le calcul functionnel
- Akkar, M.; El Kinani, A.; Oudades, M.
We show that the Banach algebras with continuous involution are the Banach algebras which admit a harmonic functional calculus, while we prove that the hermitian commutative Banach algebras are exactly the involutive commutative Banach algebras that admit a real analytic functional calculus
115.
A new class of nonassociative algebras with involution
- Kamiya, Noriaki; Mondoc, Daniel
This article is devoted to introduce a new class of nonassociative algebras with involution including the class of structurable algebras.
116.
Poisson algebras associated to quasi-Hopf algebras
- Enriquez, B.; Halbout, G.
We define admissible quasi-Hopf quantized universal enveloping (QHQUE)
algebras by h-adic valuation conditions. We show that any QHQUE algebra is
twist-equivalent to an admissible one. We prove a related statement: any
associator is twist-equivalent to a Lie associator. We attach a quantized
formal series algebra to each admissible QHQUE algebra and study the resulting
Poisson algebras.
117.
Generalized Path Algebras and Pointed Hopf Algebras
- Zhang, Shouchuan; Zhang, Yao-Zhong; Guo, Xijing
Most of pointed Hopf algebras of dimension $p^m$ with large coradical are
shown to be generalized path algebras. By the theory of generalized path
algebras it is obtained that the representations, homological dimensions and
radicals of these Hopf algebras. The relations between the radicals of path
algebras and connectivity of directed graphs are given.
118.
Algebre de Clifford d'un antiautomorphisme
- Cortella, Anne
We give a definition of the Clifford algebra of an antiautomorphism of a
central simple algebra, and compute it for the algebras of degree 2.
119.
Relation Algebra with Binders
Abstract The language of relation algebras is expanded with variables denoting individual elements in the domain and with the # binder from hybrid logic. Every elementary property of binary relations is expressible in the resulting language, something which fails for the relation algebraic language. That the new language is natural for speaking about binary relations is indicated by the fact that both Craig's Interpolation, and Beth's Definability theorem hold for its set of validities. The paper contains a number of worked out examples.
120.
Simple Conformal Algebras Generated by Jordan Algebras
- Xu, Xiaoping
In this article, we first give a short introduction to conformal algebras.
Then we present three families of simple conformal algebras finite growth
generated by simple Jordan algebras of types A, B, C.
