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Generalized bialgebras and triples of operads
, 2006
"... Key words and phrases. Bialgebra, generalized bialgebra, Hopf algebra, Cartier-Milnor-Moore, Poincaré-Birkhoff-Witt, operad, prop, triple of operads, primitive part, dendriform algebra, duplicial algebra, pre-Lie ..."
Abstract
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Cited by 12 (2 self)
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Key words and phrases. Bialgebra, generalized bialgebra, Hopf algebra, Cartier-Milnor-Moore, Poincaré-Birkhoff-Witt, operad, prop, triple of operads, primitive part, dendriform algebra, duplicial algebra, pre-Lie
DEFORMATION THEORY OF REPRESENTATIONS OF PROP(ERAD)S I
"... Abstract. In this paper and its follow-up [MV08], we study the deformation theory of morphisms of properads and props thereby extending Quillen’s deformation theory for commutative rings to a non-linear framework. The associated chain complex is endowed with an L∞-algebra structure. Its Maurer-Carta ..."
Abstract
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Cited by 7 (3 self)
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Abstract. In this paper and its follow-up [MV08], we study the deformation theory of morphisms of properads and props thereby extending Quillen’s deformation theory for commutative rings to a non-linear framework. The associated chain complex is endowed with an L∞-algebra structure. Its Maurer-Cartan elements correspond to deformed structures, which allows us to give a geometric interpretation of these results.
Operads of compatible structures and weighted partitions
- J. Pure Appl. Algebra
"... Abstract. In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large class of algebraic structures by using the poset meth ..."
Abstract
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Cited by 1 (0 self)
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Abstract. In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large class of algebraic structures by using the poset method of B. Vallette. In particular we show that this is true for the operads of compatible Lie, associative and pre-Lie algebras.
Theorem (Gerstenhaber).
"... For f ∈ Hom(V ⊗n, V) and g ∈ Hom(V ⊗m, V), binary product f ⋆ g:= n∑ i=1 ..."
DEFORMATION THEORY OF REPRESENTATIONS OF PROP(ERAD)S II
"... Abstract. This paper is the follow-up of [MV08]. ..."
