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In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
These lectures describe Hecke algebra isomorphisms and types for depth-zero principal series blocks, a.k.a. Bernstein components Rs(G) for s = sχ = [T, χe]G, where χ is a depth-zero character on T(O...
MATH 603: INTRODUCTION TO COMMUTATIVE ALGEBRA     MATH  COMMUTATIVE ALGEBRA       font style='font-size:12px;'> 2015/9/29
What is this course about? The foundations of di erential geometry (= study of manifolds) rely on analysis in several variables as \local machinery": many global theorems about manifolds are reduced...
A FIRST LOOK AT DIFFERENTIAL ALGEBRA     DIFFERENTIAL ALGEBRA       font style='font-size:12px;'> 2015/8/26
A FIRST LOOK AT DIFFERENTIAL ALGEBRA.
We analyze the structure of theMalvenuto-Reutenauer Hopf algebraSSym of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primiti...
STRUCTURE OF THE LODAY-RONCO HOPF ALGEBRA OF TREES     Hopf algebra  planar binary tree  permutation  weak order       font style='font-size:12px;'> 2015/8/14
Loday and Ronco defined an interesting Hopf algebra structure on the linear span of the set of planar binary trees. They showed that the inclusion of the Hopf algebra of non-commutative symmetric fu...
Combinatorics of the free Baxter algebra     free Baxter algebra  Combinatorics       font style='font-size:12px;'> 2015/8/14
We study the free (associative, non-commutative) Baxter algebra on one generator. The first explicit description of this object is due to Ebrahimi-Fard and Guo. We provide an alternative description...
THE PEAK ALGEBRA AND THE DESCENT ALGEBRAS OF TYPES B AND D     peak algebra  signed permutations  Coxeter groups       font style='font-size:12px;'> 2015/8/14
We show the existence of a unital subalgebra Pn of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show that Pn is the...
We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a fact...
A GROWTH MODEL,A GAME,AN ALGEBRA,LAGRANGE INVERSION,AND CHARACTERISTIC CLASSES.
Analysis of Systematic Scan Metropolis Algorithms Using Iwahori–Hecke Algebra Techniques。
On Hopf algebra structures over operads     Hopf algebra  operads       font style='font-size:12px;'> 2015/3/25
We study P-Hopf algebras with one coassociative cooperation over different operads P. For example, we consider the Loday-Ronco dendriform Hopf algebra and its isomorphisms with the noncommutative plan...
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended ...
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to ...
Learning to Automatically Solve Algebra Word Problems     Algebra Word Problems  Automatically       font style='font-size:12px;'> 2014/11/26
Learning to Automatically Solve Algebra Word Problems。

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