Twisted Actions and Obstructions in Group Cohomology

Raeburn, Iain; Sims, Aidan; Williams, Dana P.

doi:10.1007/978-3-642-57288-3_9

Cited by 8 publications

(10 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can take u(x, y) = 1 whenever x or y is the identity. This is almost precisely the data needed to define a Busby-Smith (or Leptin) twisted crossed product A ⋊ α,u G of A and G, [24,7,32]. Assuming that u is a measurable function on G × G, we can define a twisted convolution product and adjoint on C 0 (G, A) by…”

Section: Generalised Busby-smith Twisted Crossed Productsmentioning

confidence: 99%

Nonassociative Tori and Applications to T-Duality

Bouwknegt

Hannabuss²,

Mathai

2006

Commun. Math. Phys.

118

229

View full text Add to dashboard Cite

Abstract. In this paper, we initiate the study of C * -algebras A endowed with a twisted action of a locally compact Abelian Lie group G, and we construct a twisted crossed product A⋊G, which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to T-duality in Type II string theory to obtain the T-dual of a general principal torus bundle with general H-flux, which we will argue to be a bundle of noncommutative, nonassociative tori. We also show that this construction of the T-dual includes all of the special cases that were previously analysed.

show abstract

Section: Generalised Busby-smith Twisted Crossed Productsmentioning

confidence: 99%

Nonassociative Tori and Applications to T-Duality

Bouwknegt

Hannabuss²,

Mathai

2006

Commun. Math. Phys.

118

229

View full text Add to dashboard Cite

show abstract

“…His invariants consist of a normal subgroup N, and λ, µ satisfying these equations. A nice review of this circle of ideas is [69]. Incidentally, in section 4.9 we need the converse, that any solution λ, µ comes from a ψ in this way.…”

Section: Qed To Claimmentioning

confidence: 99%

Reconstruction and local extensions for twisted group doubles, and permutation orbifolds

Evans¹,

Gannon²

2021

Preprint

View full text Add to dashboard Cite

We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational conformal net. We also show that any twisted double of a solvable group is the category of modules of a completely rational vertex operator algebra. In the process of doing this, we identify the 3-cocycle twist for permutation orbifolds of holomorphic conformal nets: unexpectedly, it can be nontrivial, and depends on the value of the central charge modulo 24. In addition, we determine the branching coefficients of all possible local (conformal) extensions of any finite group orbifold of holomorphic conformal nets, and identify their modular tensor categories. All statements also apply to vertex operator algebras, provided the conjecture holds that finite group orbifolds of holomorphic VOAs are rational, with a category of modules given by a twisted group double.

show abstract

“…In [7] non-Hausdorff symmetry groups are described by crossed modules. Crossed modules are already considered in [22] in order to study some obstruction problems for twisted actions cohomologically. Since crossed modules are equivalent to strict 2-groups, their appearance in [7,22] is of fundamental importance.…”

Section: Out(a) := Aut(a) Inn(a)mentioning

confidence: 99%

“…Crossed modules are already considered in [22] in order to study some obstruction problems for twisted actions cohomologically. Since crossed modules are equivalent to strict 2-groups, their appearance in [7,22] is of fundamental importance. The general theory of 2-categories explains various definitions related to twisted group actions, and it even provides some insights for ordinary group actions.…”

Section: Out(a) := Aut(a) Inn(a)mentioning

confidence: 99%

A higher category approach to twisted actions on c^* -algebras

Buss¹,

Zhu²,

Meyer³

2012

Proceedings of the Edinburgh Mathematical Society

View full text Add to dashboard Cite

Abstract. C * -algebras form a 2-category with * -homomorphisms or correspondences as morphisms and unitary intertwiners as 2-morphisms. We use this structure to define weak actions of 2-categories, weakly equivariant maps between weak actions, and modifications between weakly equivariant maps. In the group case, we identify the resulting notions with known ones, including Busby-Smith twisted actions and equivalence of such actions, covariant representations, and saturated Fell bundles. For 2-groups, weak actions combine twists in the sense of Green and Busby-Smith.The Packer-Raeburn Stabilisation Trick implies that all Busby-Smith twisted group actions of locally compact groups are Morita equivalent to classical group actions. We generalise this to actions of strict 2-groupoids.

show abstract

Twisted Actions and Obstructions in Group Cohomology

Cited by 8 publications

References 24 publications

Nonassociative Tori and Applications to T-Duality

Nonassociative Tori and Applications to T-Duality

Reconstruction and local extensions for twisted group doubles, and permutation orbifolds

A higher category approach to twisted actions on c^* -algebras

Contact Info

Product

Resources

About

Twisted Actions and Obstructions in Group Cohomology

Cited by 8 publications

References 24 publications

Nonassociative Tori and Applications to T-Duality

Nonassociative Tori and Applications to T-Duality

Reconstruction and local extensions for twisted group doubles, and permutation orbifolds

A higher category approach to twisted actions on c* -algebras

Contact Info

Product

Resources

About

A higher category approach to twisted actions on c^* -algebras