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pro vyhledávání: '"Lucio, Victor Roca i"'
Autor:
Calaque, Damien, Lucio, Victor Roca i
This is a survey on Drinfeld associators and their generalizations, where we focus on operadic aspects.
Comment: 78 pages. Minor improvements due to referee comments
Comment: 78 pages. Minor improvements due to referee comments
Externí odkaz:
http://arxiv.org/abs/2402.05539
The aim of this note is to give a detailed account of how symmetric operads can be constructed from planar (non-symmetric) operads, and to carefully spell out the algebraic interplay between these two notions. It is a companion note to the main paper
Externí odkaz:
http://arxiv.org/abs/2312.05005
Algebraic operads provide a powerful tool to understand the homotopy theory of the types of (co)algebras they encode. So far, the principal results and methods that this theory provides were only available in characteristic zero. The reason is that o
Externí odkaz:
http://arxiv.org/abs/2310.13095
Autor:
Lucio, Victor Roca i
The main goal of this article is to develop integration theory over a positive characteristic field, and as a by-product, construct Lie-type models for the $p$-adic homotopy types of spaces. We introduce a new type of algebraic structure called curve
Externí odkaz:
http://arxiv.org/abs/2306.07829
The main goal of this paper is to introduce a framework for infinitesimal deformation problems, using new methods coming from operadic calculus. We construct an adjunction between infinitesimal deformation problems over some type of algebras and thei
Externí odkaz:
http://arxiv.org/abs/2306.07227
Autor:
Lucio, Victor Roca i
In this article, we introduce the notion of a curved absolute $\mathcal{L}_\infty$-algebra, a structure that behaves like a curved $\mathcal{L}_\infty$-algebra where all infinite sums of operations are well-defined by definition. We develop their int
Externí odkaz:
http://arxiv.org/abs/2209.10282
Autor:
Lucio, Victor Roca i
Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as algebras o
Externí odkaz:
http://arxiv.org/abs/2209.09833
Autor:
Lucio, Victor Roca i
The main goal of this thesis is to develop the integration theory of curved homotopy Lie algebras. In the first chapter, we develop the operadic calculus needed: we encode non-necessarily conilpotent coalgebras with operads and introduce their dual n
Externí odkaz:
http://arxiv.org/abs/2207.11115
Autor:
Lucio, Victor Roca i
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus at this ne
Externí odkaz:
http://arxiv.org/abs/2201.07155
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