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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...
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       font style='font-size:12px;'> 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       font style='font-size:12px;'> 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...
Pre-Lie algebras and the rooted trees operad     Pre-Lie algebras  rooted trees operad       font style='font-size:12px;'> 2015/3/25
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...
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...
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...
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...
On the structure of cofree Hopf algebras     cofree Hopf algebras       font style='font-size:12px;'> 2015/3/25
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...
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       font style='font-size:12px;'> 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...
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       font style='font-size:12px;'> 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...
Why Banach algebras?     Banach algebras  History and Overview  Functional Analysis       font style='font-size:12px;'> 2012/6/27
We give a brief overview of the area of Banach algebras, intended for a general mathematical audience.
Rohlin flows on von Neumann algebras     Rohlin flows  von Neumann algebras  Operator Algebras       font style='font-size:12px;'> 2012/6/21
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 ...

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