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We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bi...
Derivations and Projections on Jordan Triples. An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis
Derivations and Projections Jordan Triples nonassociative algebra continuous cohomology quantum functional analysis Operator Algebras
2012/6/19
This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-1...
Ternary Weakly Amenable C*-algebras and JB*-triples
C*-algebras and JB*-triples Operator Algebras
2012/6/19
A well known result of Haagerup from 1983 states that every C*-algebra A is weakly amenable, that is, every (associative) derivation from A into its dual is inner. A Banach algebra B is said to be ter...
Upgrading Subgroup Triple Product Property Triples
Subgroup Triple Product Property Triples Group Theory
2011/9/23
Abstract: In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group $G$ satisfying the Triple Product Property (TPP) as...
Abstract: Using ultrafilter techniques we show that in any partition of $\mathbb{N}$ into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $a,b,a^b$ (...
The Group of Primitive Almost Pythagorean Triples
Almost pythagorean triples Infinitely generated commutative groups Number Theory
2011/9/6
Abstract: We consider the triples of integer numbers that are solutions of the equation $x^2+qy^2=z^2$, where $q$ is a fixed, square-free arbitrary positive integer. The set of equivalence classes of ...
A New Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples
elliptic curves rank pythagorean triples
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves in the form of y2 = x(x−a2)(x−b2) that have positive ranks. We first generate a list of pythagorean triples (a, b, c) ...
Manin triples and differential operators on quantum groups
Manin triples differential operators quantum groups
2011/1/18
Let (a,m, l) be a Manin triple, and let M, L be algebraic groups with Lie algebras m, l respectively. We point out that the product M×L carries a natural structure of Poisson manifold,whose Poisson te...
Toric CFTs, Permutation Triples, and Belyi Pairs
Toric CFTs Permutation Triples Belyi Pairs
2011/3/2
Four-dimensional CFTs dual to branes transverse to toric Calabi{Yau threefolds have been described by bipartite graphs on a torus (dimer models). We use the theory of dessins d'enfants to describe the...
We construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the...
Spectral triples for finitely presented groups, index 1
Spectral triples finitely presented groups
2010/11/23
Using generalized Cayley graphs and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index $1$.
Spectral triples for hyperbolic dynamical systems
Spectral triples hyperbolic dynamical systems
2010/11/19
Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topolog...
Spectral triples and Gibbs measures for expanding maps on Cantor sets
spectral triple Dixmier trace expanding map Gibbs measure
2010/12/14
Let T : ! be an expanding map on a Cantor set. For each suitably normalized H¨older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as ...
COMPARISON OF INVARIANTS FOR TRIPLES OF HILBERT SPACES
COMPARISON OF INVARIANTS HILBERT SPACES
2010/3/17
In [2,3] the sequence of invariant characteristics (mm) for the finite families of Hilbert spaces were considered. Here we make a comparison of these invariants among themselves. We construct some exa...