Zobrazeno 1 - 10
of 69
pro vyhledávání: '"Lauve, Aaron"'
Autor:
Lauve, Aaron, Reutenauer, Christophe
Publikováno v:
Noncommutative birational geometry, representations and combinatorics, pp. 177-197, Contemp. Math., v. 592, Amer. Math. Soc., Providence, RI, 2013
We characterize rational series over the free group by using an operator introduced by A. Connes. We prove that rational Malcev--Neumann series posses rational expressions without simplifications. Finally, we develop an effective algorithm for solvin
Externí odkaz:
http://arxiv.org/abs/1806.03540
Autor:
Lauve, Aaron, Mastnak, Mitja
We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we study proper
Externí odkaz:
http://arxiv.org/abs/1803.02691
Publikováno v:
L'Enseignement Mathematique (2) 64 (2018), 23-63
Any multiplicity-free family of finite dimensional algebras has a canonical complete set of of pairwise orthogonal primitive idempotents in each level. We give various methods to compute these idempotents. In the case of symmetric group algebras over
Externí odkaz:
http://arxiv.org/abs/1606.08900
Autor:
Aguiar, Marcelo, Lauve, Aaron
Publikováno v:
Algebra Number Theory 9 (2015) 547-583
The Adams operators $\Psi_n$ on a Hopf algebra $H$ are the convolution powers of the identity of $H$. We study the Adams operators when $H$ is graded connected. They are also called Hopf powers or Sweedler powers. The main result is a complete descri
Externí odkaz:
http://arxiv.org/abs/1403.7584
Autor:
Hangelbroek, Thomas, Lauve, Aaron
The purpose of this article is to provide a solution to the $m$-fold Laplace equation in the half space $R_+^d$ under certain Dirichlet conditions. The solutions we present are a series of $m$ boundary layer potentials. We give explicit formulas for
Externí odkaz:
http://arxiv.org/abs/1305.5063
Autor:
Konvalinka, Matjaz, Lauve, Aaron
We produce skew Pieri Rules for Hall--Littlewood functions in the spirit of Assaf and McNamara. The first two were conjectured by the first author. The key ingredients in the proofs are a q-binomial identity for skew partitions and a Hopf algebraic i
Externí odkaz:
http://arxiv.org/abs/1201.1404
Autor:
Aguiar, Marcelo, Lauve, Aaron
Publikováno v:
Can. J. Math.-J. Can. Math. 65 (2013) 241-265
Following Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange's theorem for Hopf monoids in the category of connected species. As a corollary, we obtain necessary conditions for a given subspecies K of a Hopf monoid H t
Externí odkaz:
http://arxiv.org/abs/1105.5572
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and in the theory of species. We prove that the composition of two cofree coalgebras is again cofree, and we give sufficient conditions that
Externí odkaz:
http://arxiv.org/abs/1012.3483
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree coalgebras is cofree and give conditions which imply that the composit
Externí odkaz:
http://arxiv.org/abs/1011.4305
Autor:
Aguiar, Marcelo, Andre, Carlos, Benedetti, Carolina, Bergeron, Nantel, Chen, Zhi, Diaconis, Persi, Hendrickson, Anders, Hsiao, Samuel, Isaacs, I. Martin, Jedwab, Andrea, Johnson, Kenneth, Karaali, Gizem, Lauve, Aaron, Le, Tung, Lewis, Stephen, Li, Huilan, Magaard, Kay, Marberg, Eric, Novelli, Jean-Christophe, Pang, Amy, Saliola, Franco, Tevlin, Lenny, Thibon, Jean-Yves, Thiem, Nathaniel, Venkateswaran, Vidya, Vinroot, C. Ryan, Yan, Ning, Zabrocki, Mike
Publikováno v:
Advances in Mathematics 229 (2012) 2310--2337
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 the ring of symmetric functions in noncommuting variab
Externí odkaz:
http://arxiv.org/abs/1009.4134