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Co-H-structures on equivariant Moore spaces

Martin Arkowitz, Marek Golasiński (1994)

Fundamenta Mathematicae

Let G be a finite group, 𝕆 G the category of canonical orbits of G and A : 𝕆 G → 𝔸 b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with E x t n - 1 ( A , A ⊗ A ) . Then the case G = ℤ p k leads to an example of infinitely...

De Rham cohomology and homotopy Frobenius manifolds

Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette (2015)

Journal of the European Mathematical Society

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.

Derivations of homotopy algebras

Tom Lada, Melissa Tolley (2013)

Archivum Mathematicum

We recall the definition of strong homotopy derivations of A ∞ algebras and introduce the corresponding definition for L ∞ algebras. We define strong homotopy inner derivations for both algebras and exhibit explicit examples of both.

Examples of homotopy Lie algebras

Klaus Bering, Tom Lada (2009)

Archivum Mathematicum

We look at two examples of homotopy Lie algebras (also known as L ∞ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators Δ to verify the homotopy Lie data is shown to produce the same results.

Explicit cogenerators for the homotopy category of projective modules over a ring

Amnon Neeman (2011)

Annales scientifiques de l'École Normale Supérieure

Let R be a ring. In two previous articles [12, 14] we studied the homotopy category 𝐊 ( R - Proj ) of projective R -modules. We produced a set of generators for this category, proved that the category is ℵ 1 -compactly generated for any ring R , and showed that it need not always be compactly generated, but is for sufficiently nice R . We furthermore analyzed the inclusion j ! : 𝐊 ( R - Proj ) → 𝐊 ( R - Flat ) and the orthogonal subcategory 𝒮 = 𝐊 ( R - Proj ) ⊥ . And we even showed that the inclusion 𝒮 → 𝐊 ( R - Flat ) has a right adjoint; this forces some natural map to be an equivalence...

Free A ∞ -categories.

Lyubashenko, Volodymyr, Manzyuk, Oleksandr (2006)

Theory and Applications of Categories [electronic only]

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