81.
Alternative Noetherian Banach Algebras
- Benslimane, M.; Boudi, N.
Sinclair and Tullo [6] proved that noetherian Banach algebras are finite-dimensional. In [3], Grabiner studied noetherian Banach modules. In this paper, we are concerned with alternative noetherian Banach algebras. Combining techniques from [3] with techniques and the result from [6], we prove that every alternative noetherian Banach algebra is finite-dimensional.
82.
Vertex algebras
- Borcherds, Richard E.
In this paper we try to define the higher dimensional analogues of vertex
algebras. In other words we define algebras which we hope have the same
relation to higher dimensional quantum field theories that vertex algebras have
to one dimensional quantum field theories (or to ``chiral halves'' of two
dimensional quantum field theories). The main idea is to define "vertex
groups". Then classical vertex algebras turn out to be the same as "associative
commutative algebras" over the simplest nontrivial example of a vertex group.
We investigate commutative algebras over higher dimensional vertex groups, some
of which seem to be closely related to (free) quantum field theories.
83.
Associative Algebra -- from MathWorld
- Weisstein, Eric W.
In simple terms, let x, y, and z be members of an algebra. Then the algebra is said to be associative if x\cdot(y\cdot z) = (x\cdot y)\cdot z, where \cdot denotes multiplication. More formally, let A denote an \mathbb{R}-algebra, so that A is a vector space over \mathbb{R} and A\times A\to A (x,y)\mapsto x\cdot y. Then A is said to be m-associative if there exists an m-dimensional subspace S of A such that (y\cdot x)\cdot z=y\cdot(x\cdot z) for all y, z\in A and x\in S. Here, vector...
84.
Homology of ...-algebras and Cyclic Homology
- Masoud Khalkhali; A Algebras; Let T
this paper is to lay the ground such that an extension of this theorem to the category of A1 -algebras becomes possible (theorem 3.1). The category of L1 - (respectively, A1 -) algebras extend the category of differential graded (DG) Lie (respectively, DG associative) algebras. These concepts are both due to J. Stasheff. See [S], [LS], and references therein, and also [HS] where an alternative approach to L1 -algebras is given. In [Kh], we proposed an approach to homological invariants of A1 - algebras (Hochschild, cyclic, periodic cyclic, etc.) based on the notion of X-complex due to Cuntz and Quillen...
85.
Differential Schemes
- E. Kolchin Dierential Algebra,Algebraic Groups
ia) 33 (1978), 1-17.
[5] G. Carra' Ferro The ring of global sections of the structure sheaf on
the dierential spectrum, Rev. Roumaine Math. Pures Appl. 30 (1985),
809-814.
[6] G. Carra' Ferro Kolchin schemes, J. Pure and Applied Alg. 63 (1990),
13-27.
[7] P. Cassidy Dierential algebraic groups, Amer. J. Math. 94 (1972), 891{
954.
[8] H. Gorman Dierential Rings and Modules, Scripta Math. 29 (1973),
25-35.
[9] I. Kaplansky An Introduction to Dierential Algebra, Hermann,
Paris, 1957.
[10] W. Keigher Adjunctions and comonads in dierential algebra, Pacic J. Math. 92 (1982),
281-293.
[2] A. Buium Dierential functions
References
86.
Boolean Algebra -- from MathWorld
- Weisstein, Eric W.
A mathematical structure which is similar to a Boolean ring, but which is defined using the meet and join operators instead of the usual addition and multiplication operators. Explicitly, a Boolean algebra is the partial order on subsets defined by inclusion (Skiena 1990, p. 207), i.e., the Boolean algebra b(A) of a set A is the set of subsets of A that can be obtained by means of a finite number of the set operations union (OR), intersection (AND), and complementation (NOT) (Comtet 1974, p....
87.
Partial Algebra -- from MathWorld
- Weisstein, Eric W.
A partial algebra is a pair \mathbb{A}=\left(A,\left(f_i^{\mathbb{A}}\right)_i\in I\right), where for each i\in I, there are an ordinal \alpha_i and a set X_i\subseteq A^{\alpha_i} such that f_i^{\mathbb{A}} is a function from X_i into A. In case X_i=A^{\alpha_i}, the operation f_i^{\mathbb{A}} is called a total operation, and otherwise, it is called a partial operation. See also: Topological Partial Algebra
88.
Nonrepresentable Sequential Algebras
- Peter Jipsen; Roger D. Maddux
The sequential calculus of von Karger and Hoare [18] is designed for reasoning about sequential phenomena, dynamic or temporal logic, and concurrent or reactive systems. Unlike the classical calculus of relations, it has no operation for forming the converse of a relation. Sequential algebras [15] are algebras that satisfy certain equations in the sequential calculus. One standard example of a sequential algebra is the set of relations included in a partial ordering. Nonstandard examples arise by relativizing relation algebras to elements that are antisymmetric, transitive, and reflexive. The incompleteness and non-finite-axiomatizability of the sequential calculus are examined here from a...
89.
Topological Partial Algebra -- from MathWorld
- Weisstein, Eric W.
A topological partial algebra is a pair (\mathbb{A},\tau), where \mathbb{A}=\left(A,(f_i^{\mathbb{A}})_i\in I\right) is a partial algebra and each of the operations f_i^{\mathbb{A}} is continuous in the product topology. Examples of topological partial algebras include topological groups, topological vector spaces, and topological fields. Specifically, a topological field is an example of a topological partial algebra that is not a topological algebra in the strict sense of the term. See...
90.
Quantum affine algebras and affine Hecke algebras
- Chari, Vyjayanthi; Pressley, Andrew
We describe a connection between finite--dimensional representations of
quantum affine algebras and affine Hecke algebras.
91.
One-parametric selfinjective algebras
- BOCIAN, Rafa?; SKOWRO?SKI, Andrzej
In continuation of our papers [5], [6] we complete the classification of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings.
92.
Robbins Algebras vs. Boolean Algebras
- Adam Grabowski
In the early 1930s, Huntington proposed several axiom systems for
Boolean algebras. Robbins slightly changed one of them and asked if the
resulted system is still a basis for variety of Boolean algebras. Partial
solution has been given by Winker in 1992 and in 1996 McCune with the
help of theorem prover gave the positive answer. Some simplified and
restructurized versions of this proof are known. We describe in this paper
some of the issues concerned with full mechanically checked proof of the
fact that all Robbins algebras are Boolean.
93.
Polar decomposition in Rickart C*-algebras
- Goldstein, Dmitry
A new proof is obtained to the following fact: a Rickart $C^*$-algebra satisfies polar decomposition. Equivalently, matrix algebras over a Rickart $C^*$-algebra are also Rickart $C^*$-algebras.
94.
Double Poisson algebras
- Bergh, Michel Van den
In this paper we show that the moduli spaces of representations associated to
the deformed multiplicative preprojective algebras recently introduced by
Crawley-Boevey and Shaw carry a natural Poisson structure. This follows the
fact that appropriately localized path algebras of double quivers carry a
certain kind of non-commutative quasi-Hamiltonian structure.
95.
Generalized double tilted algebras
- REITEN, Idun; SKOWRO?SKI, Andrzej
We introduce the class of generalized double tilted artin algebras and prove that it coincides with the class of artin algebras whose $\mathrm{AR}$ -quiver admits a faithful generalized standard almost directed component. A homological characterization of faithful generalized standard almost directed components is also established.
96.
La enseñanza de álgebra con NTIC en la universidad
- Acosta, Julio C.; Macías, Dora A.; La Red Martínez, David
Se trata de un proyecto de investigación en educación a distancia en un curso de Álgebra en la Universidad, usando los recursos tecnológicos disponibles. este trabajo explica desde la realidad de la Asignatura Matemática I (Álgebra) y de nuestros alumnos -destinatarios del curso-, el diseño de un material multimedia con los contenidos propios de la asignatura, que se usa como herramienta en el proceso de enseñanza- aprendizaje y cómo funciona nuestra aula virtual y nuestro curso a distancia. Se describen un material multimedia diseñado al efecto y el inicio de la segunda etapa de la experiencia-innovación, con el diseño y...
97.
On poset Boolean algebras
- Uri Abraham; Robert Bonnet; Matatyahu Rubin
Let 〈P, ≤ 〉 be a partially ordered set. The poset Boolean algebra of P, denoted F (P), is defined as follows: The set of generators of F (P) is {xp: p ∈ P}, and the set of relations is {xp · xq = xp: p ≤ q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and 〈G, ≤ B ↾G 〉 is well-founded. A well-generated algebra is superatomic. Theorem 1. Let 〈P, ≤ 〉 be a partially ordered set. The following are equivalent. (i) P does not...
98.
Elliptic algebras
- Odesskii, Alexander
The survey is devoted to associative $\Z_{\ge0}$-graded algebras presented by
n generators and n(n-1)/2 quadratic relations and satisfying the so-called
Poincare-Birkhoff-Witt condition (PBW-algebras). We consider examples of such
algebras depending on two continuous parameters (namely, on an elliptic curve
and a point on this curve) which are flat deformations of the polynomial ring
in n variables. Diverse properties of these algebras are described, together
with their relations to integrable systems, deformation quantization, moduli
spaces and other directions of modern investigations.
99.
Subalternative Algebras
- A. Cedilnik
. An algebra is called subalternative if the associator of any three
linearly dependent elements is their linear combination. We prove that in characteristic
100.
Associative algebras related to conformal algebras
- Kolesnikov, Pavel
In this note, we introduce a class of algebras that are in some sense related
to conformal algebras. This class (called TC-algebras) includes Weyl algebras
and some of their (associative and Lie) subalgebras. By a conformal algebra we
generally mean what is known as $H$-pseudo-algebra over the polynomial Hopf
algebra $H=\Bbbk[T_1,..., T_n]$. Some recent results in structure theory of
conformal algebras are applied to get a description of TC-algebras.
