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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
noncommuting variables related Hopf algebras
2015/8/14
We identify two seemingly disparate structures: supercharacters, a useful way of doing
Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite
field, and th...
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
The coefficient matrix and symmetric function hopf algebra
2015/7/7
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a fi-nite ...
Hopf algebras and Markov chains: Two examples and a theory
By-products hopf algebra markov chain complex lie algebra combination
2015/7/7
The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied meth...
Quadri-algebras
Quadri-algebras
2015/3/25
We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner. We present several...
A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatoria...
Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras
Operadic formulation topological vertex algebras Gerstenhaber Batalin-Vilkovisky algebras
2015/3/25
We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we...
Open-string vertex algebras, tensor categories and operads
Open-string vertex algebras tensor categories operads
2015/3/25
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the n...
Deformations of algebras over operads and Deligne's conjecture
algebras over operads Deligne's conjecture
2015/3/25
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of...
We prove an analogue of the Poincare'-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a B-infini-algeb...
Manin products, Koszul duality, Loday algebras and Deligne conjecture
Manin products Koszul duality Loday algebras Deligne conjecture
2015/3/25
In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric o...
Hecke Algebras
Hecke Algebras
2015/7/6
By a Hecke Algebra we will usually mean an Iwahori Hecke algebra. We will now
explain what these are. A Coxeter group consist of data (W; I) where W is a group
and I = fs1; ; srg of elements o...
Does the theory of tracial von Neumann algebras have a model companion?
the theory of tracial von Neumann algebras model companion Logic
2012/7/11
In this note, we show that, assuming a positive solution to the Connes Embedding Problem (CEP), the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fa...
A colimit decomposition for homotopy algebras in Cat
A colimit decomposition homotopy algebras Cat Category Theory
2012/6/25
Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky o...
We give a brief overview of the area of Banach algebras, intended for a general mathematical audience.
We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as ...