Symmetric cohomology and symmetric Hochschild cohomology of cocommutative Hopf algebras [PDF]
Journal of Algebra and Its Applications (2023), 2022 Staic defined symmetric cohomology of groups and studied that the secondary symmetric cohomology group is corresponding to group extensions and the injectivity of the canonical map from symmetric cohomology to classical cohomology. In this paper, we define symmetric cohomology and symmetric Hochschild cohomology for cocommutative Hopf algebras.
arxiv +1 more source
’t Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology [PDF]
Communications in Mathematical Physics, 2018 We study discrete symmetries of Dijkgraaf–Witten theories and their gauging in the framework of (extended) functorial quantum field theory. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete conditions for such a ...
L. Müller, R. Szabo
semanticscholar +1 more source
On Restricted Cohomology of Modular Classical Lie Algebras and Their Applications
Mathematics, 2022 In this paper, we study the restricted cohomology of Lie algebras of semisimple and simply connected algebraic groups in positive characteristics with coefficients in simple restricted modules and their applications in studying the connections between ...
Sherali S. Ibraev +2 more
doaj +1 more source
Bosonic crystalline symmetry protected topological phases beyond the group cohomology proposal [PDF]
, 2018 It is demonstrated by explicit construction that three-dimensional bosonic crystalline symmetry protected topological (cSPT) phases are classified by $H_{\phi}^{5}(G;\mathbb{Z})\oplus H_{\phi}^{1}(G;\mathbb{Z})$ for all 230 space groups $G$, where $H^n_ ...
Hao Song +2 more
semanticscholar +1 more source
A tight colored Tverberg theorem for maps to manifolds (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Any continuous map of an $N$-dimensional simplex $Δ _N$ with colored vertices to a $d$-dimensional manifold $M$ must map $r$ points from disjoint rainbow faces of $Δ _N$ to the same point in $M$, assuming that $N≥(r-1)(d+1)$, no $r$ vertices of $Δ _N ...
Pavle V. M. Blagojević +2 more
doaj +1 more source
On the Morse–Novikov Cohomology of blowing up complex manifolds
Comptes Rendus. Mathématique, 2020 Inspired by the recent works of S. Rao–S. Yang–X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse–Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse–Novikov cohomology by introducing the relative ...
Zou, Yongpan
doaj +1 more source
The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras
Electronic Research Archive, 2022 The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of
Shanshan Liu +2 more
doaj +1 more source
Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond. [PDF]
Physical Review Letters, 2014 The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders.
Juven C. Wang, Z. Gu, X. Wen
semanticscholar +1 more source
Algebraic Cohomology of Topological Groups [PDF]
Transactions of the American Mathematical Society, 1973 A general cohomology theory for topological groups is described, and shown to coincide with the theories of C. C. Moore [12] and other authors. We also recover some invariants from algebraic topology.
David Wigner
openalex +6 more sources
Symmetry protected topological orders and the group cohomology of their symmetry group [PDF]
, 2011 Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry.
Xie Chen, Z. Gu, Zhengxin Liu, X. Wen
semanticscholar +1 more source