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TRIPLES, ALGEBRAS AND COHOMOLOGY
 REPRINTS IN THEORY AND APPLICATIONS OF CATEGORIES
, 2003
"... ..."
Symmetric bundles and representations of Lie triple systems”, arXiv: math.DG/0710.1543
"... Abstract. We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. A symmetric bundle has an underlying reflection space, and we investigate the corresponding forgetf ..."
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Cited by 4 (4 self)
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Abstract. We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. A symmetric bundle has an underlying reflection space, and we investigate the corresponding forgetful functor both from the point of view of differential geometry and from the point of view of representation theory. This functor is not injective, as is seen by constructing “unusual ” symmetric bundle structures on the tangent bundles of certain symmetric spaces.
Composite Cotriples and Derived Functors, in
 Lecture Notes in Math
, 1969
"... The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ..."
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Cited by 4 (0 self)
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The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ground ring) and then this resolution is given the
RELATIVE HOMOLOGICAL ALGEBRA, EQUIVARIANT DE RHAM COHOMOLOGY AND KOSZUL DUALITY
, 2008
"... Abstract. We describe equivariant de Rham cohomology relative to a general (not necessarily finite dimensional compact) Lie group G in terms of a suitable differential graded Ext defined in terms of the standard construction associated with the monad arising from the assignment to a vector space V o ..."
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Abstract. We describe equivariant de Rham cohomology relative to a general (not necessarily finite dimensional compact) Lie group G in terms of a suitable differential graded Ext defined in terms of the standard construction associated with the monad arising from the assignment to a vector space V of the Vvalued de Rham complex of G. We develop a corresponding infinitesimal equivariant cohomology as the relative differential Ext with respect to the cone Cg on the Lie algebra g of G relative to g itself. Appropriate models for the differential graded Ext involving a comparison between the simplicial Weil coalgebra and the Weil coalgebra dual to the familiar ordinary Weil algebra yield small models for equivariant de Rham cohomology including the familiar Weil and Cartan models for the special case where the group is compact and connected. We explain how Koszul duality in de Rham theory results immediately
The shLie algebra perturbation Lemma
, 2009
"... Let R be a commutative ring with 1, let (M ..."
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Stacks of Anncategories and their morphisms
, 2015
"... We show that anncategories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. More precisely, we prove the groupoid of morphisms between two anncategories is equivalent to that of bimodule butterflies ..."
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We show that anncategories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. More precisely, we prove the groupoid of morphisms between two anncategories is equivalent to that of bimodule butterflies between the presentations. A bimodule butterfly is a specialization of a butterfly, i.e. a special kind of span or fraction, between the underlying complexes
Homological Algebra of Racks and Quandles
"... Contents Introduction 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 Extensions 5 1.1 Extensions and expan ..."
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Contents Introduction 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 Extensions 5 1.1 Extensions and expansions . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Factor systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Abelian extensions . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Quandle extensions . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.5 Involutory extensions . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Modules 29 2.1 Rack modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Beck modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3 A digression on Gmodules . . . . . . . . . . . . . . . . . . . . . 41 2.4 Free modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5 The rack
Wolfgang Bertram, Manon Didry 1 Symmetric bundles and representations of Lie triple systems
, 2009
"... Abstract. We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. A symmetric bundle has an underlying reflection space, and we investigate the corresponding forgetf ..."
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Abstract. We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. A symmetric bundle has an underlying reflection space, and we investigate the corresponding forgetful functor both from the point of view of differential geometry and from the point of view of representation theory. This functor is not injective, as is seen by constructing “unusual ” symmetric bundle structures on the tangent bundles of certain symmetric spaces.
Symmetric bundles and representations of Lie triple systems
"... We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. A symmetric bundle has an underlying reflection space, and we investigate the corresponding forgetful functor ..."
Abstract
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We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. A symmetric bundle has an underlying reflection space, and we investigate the corresponding forgetful functor both from the point of view of differential geometry and from the point of view of representation theory. This functor is not injective, as is seen by constructing “unusual ” symmetric bundle structures on the tangent bundles of certain symmetric spaces. 2000 MSC: 17A01, 17B10, 53C35 1