Orientation in operator algebras

A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Algebras and their arithmetics,

Reprint of the 1923 edition.

Linear algebras

Mode of access: Internet.

Arithmetica especulativa, y practica, y arte de algebra : en la qual se contiene todo lo que pertenece al arte menor, ò mercantil, y à las dos algebras, racional, è irracional, con la explicación de todas las proposiciones, y problemas de los libros quinto, septimo, octavo, nono y dezimo del principe de la matematica Euclides /

Mode of access: Internet.

Arithmetica especulativa y practiva [sic] y arte de algebra : en la qual se contiene todo lo qe pertenece al arte menor o mercantil, y a las dos algebras, racional e irracional : con la explicacion de todas las proposiciones y problemas de los libros quinto, septimo, octavo, nono y dezimo del principe de la mathematica Euclides /

Mode of access: Internet.

Arithmetica especulativa, y practica, y arte de algebra : en la qual se contiene todo lo que pertenece al arte menor, ò mercantivol, y à las dos algebras, racional, è irracional, con la explicación de todas las proposiciones, y problemas de los libros quinto, septimo, octavo, nono y decimo del principe de la matematica Euclides /

Mode of access: Internet.

Arithmetica especulativa, y practica, y arte de algebra : en la qual se contiene todo lo que pertenece al arte menor, ò mercantil, y à las dos algebras, racional, è irracional, con la explicación de todas las proposiciones, y problemas de los libros quinto, septimo, octavo, nono y dezimo del principe de la matematica Euclides /

Mode of access: Internet.

Arithmetica especulativa, y practica, y arte de algebra : en la qual se contiene todo lo que pertenece al arte menor, ò mercantil, y à las dos algebras, racional, è irracional, con la explicación de todas las proposiciones, y problemas de los libros quinto, septimo, octavo, nono y decimo del principe de la matematica Euclides /

Mode of access: Internet.

On the structure of Hopf algebras

Caption title.

Lie algebras /

"Winter 1956."

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Braided m-Lie algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End(F)M, where M is a Yetter-Drinfeld module over B with dimB < infinity. In particular, generalized classical braided m-Lie algebras sl(q,f)(GM(G)(A),F) and osp(q,l)(GM(G)(A),M,F) of generalized matrix algebra GMG(A) are constructed and their connection with special generalized matrix Lie superalgebra sl(s,f)(GM(Z2)(A(s)),F) and orthosymplectic generalized matrix Lie super algebra osp(s,l) (GM(Z2)(A(s)),M-s,F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.

Varieties of algebras arising from K-perfect m-cycle systems

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.