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Basic Hopf Algebras of Finite Representation Type and Their Classification
Basic Hopf Algebras Finite Representation Type Their Classification
2018/4/20
Let k be a algebraically closed field. We give a necessary and sufficient condition for a basic Hopf algebra over k to be finite representation type. Explicitly, we prove that a basic Hopf algebra ove...
A classification of BL-algebras.
THE SATAKE ISOMORPHISM FOR SPECIAL MAXIMAL PARAHORIC HECKE ALGEBRAS
PARAHORIC HECKE Algebra
2015/9/29
Let G denote a connected reductive group over a nonarchimedean
local field F. Let K denote a special maximal parahoric subgroup of G(F). We
establish a Satake isomorphism for the Hecke algebra...
Our aim here is to give a fairly self-contained exposition of some basic facts
about the Iwahori-Hecke algebra H of a split p-adic group G, including Bernstein’s
presentation and description of the ...
THE BASE CHANGE FUNDAMENTAL LEMMA FOR CENTRAL ELEMENTS IN PARAHORIC HECKE ALGEBRAS
PARAHORIC HECKE Algebra
2015/9/29
Let G be an unramified group over a p-adic field F, and let E/F be a finite
unramified extension field. Let θ denote a generator of Gal(E/F). This paper concerns the
ma...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. In the case of real groups, the
results refer to J. Adams, P. Trapa, M. vanLeuwen, W-L. Yee a...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. This conforms to the Lefschetz
principle which states that what is true for real groups is al...
GALOIS CONNECTIONS FOR INCIDENCE HOPF ALGEBRAS OF PARTIALLY ORDERED SETS.
Incidence Hopf algebras Galois connections
2015/8/14
An important well-known result of Rota describes the relationship between the M¨obius
functions of two posets related by a Galois connection. We present an analogous result relating
the antipodes of...
A NOTE ON STRONGLY SEPARABLE ALGEBRAS
Separable algebras invariants coinvariants coalgebras Hopf algebras
2015/8/14
Let A be an algebra over a field k. If M is an A–bimodule, we let
MA and MA denote respectively the k–spaces of invariants and coinvariants of
M, and 'M : MA
! MA be the natural map. In this note w...
A definition of prepoisson algebras is proposed, combining structures of prelie and zinbiel
algebra on the same vector space. It is shown that a prepoisson algebra gives rise to a Poisson algebra
by...
Infinitesimal Hopf algebras
Hopf algebras derivations Yang-Baxter equation Drinfeld’s double
2015/8/14
Infinitesimal bialgebras were introduced by Joni and Rota [J-R].
An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in
such a way that the comultiplication is a derivation. I...
INFINITESIMAL BIALGEBRAS, PRE-LIE AND DENDRIFORM ALGEBRAS
Infinitesimal bialgebras pre-Lie algebras dendriform algebras
2015/8/14
We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal
bialgebra. We show that they correspond to modules and bimodules over the infinitesimal
version of the d...
QUADRI-ALGEBRAS
quadri-algebra operad Koszul duality
2015/8/14
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 sever...
Representations of matched pairs of groupoids and applications to weak Hopf algebras
groupoids and applications algebras
2015/8/14
We introduce the category of set-theoretic representations of a
matched pair of groupoids. This is a monoidal category endowed with a
monoidal functor f` to the category of quivers over the common b...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary
trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We
give explicit isomorphisms showing that the asso...