منابع مشابه
and triples of operads
We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its primitive part. This structure theorem extends the classical Poincaré-Birkhoff-Witt theorem and the Cartier-Milnor-Moore theorem, valid for cocommutative bia...
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We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors F : A → MA from a pointed category with coproducts to A-modules in terms of differentials of F . Here A is a commutative S-algebra. We specialize to the case when A is the category of a-algebras for an operad a and F is the forgetful functor, and derive mild...
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We develop a cohomology theory for Jordan triples, including the infinite dimensional ones, by means of the cohomology of TKK Lie algebras. This enables us to apply Lie cohomological results to the setting of Jordan triples.
متن کاملInfinitesimal or Cocommutative Dipterous Bialgebras and Good Triples of Operads
The works of Poincaré, Birkhoff, Witt and Cartier, Milnor, Moore on the connected cocommutative Hopf algebras translated in the language of operads means that the triple of operads (Com,As, Lie) endowed with the Hopf compatiblity relation is good. In this paper, we focus on left dipterous (resp. right dipterous) algebras which are associative algebras with an extra left (resp. right) module on ...
متن کاملColored operads, series on colored operads, and combinatorial generating systems
A new sort of combinatorial generating system, called bud generating system, is introduced. Bud generating systems are devices for specifying sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous grammars, allowing to work with all these generating systems in a unified way. The theory of bud generating sy...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8368