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
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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
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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
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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
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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
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Anomalous discrete symmetries in three dimensions and group cohomology. [PDF]
Physical Review Letters, 2014 We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry.
A. Kapustin, Ryan Thorngren
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Oriented Algebras and the Hochschild Cohomology Group
Mathematics, 2018 Koam and Pirashivili developed the equivariant version of Hochschild cohomology by mixing the standard chain complexes computing group with associative algebra cohomologies to obtain the bicomplex C ˜ G * ( A , X ).
Ali N. A. Koam
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Construction and field theory of bosonic-symmetry-protected topological states beyond group cohomology [PDF]
, 2015 We construct a series of bbosonic-symmetry-protected topological (BSPT) states beyond group cohomology classification using ``decorated defects'' approach.
Zhen Bi, Cenke Xu
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Second Module Cohomology Group of Induced Semigroup Algebras [PDF]
Sahand Communications in Mathematical Analysis, 2021 For a discrete semigroup $ S $ and a left multiplier operator $T$ on $S$, there is a new induced semigroup $S_{T}$, related to $S$ and $T$. In this paper, we show that if $T$ is multiplier and bijective, then the second module cohomology groups ...
Mohammad Reza Miri +2 more
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On algebraic characterizations for finiteness of the dimension of EG [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2008 Certain algebraic invariants of the integral group ring ZG of a group G were introduced and investigated in relation to the problem of extending the Farrell-Tate cohomology, which is defined for the class of groups of finite virtual cohomological ...
Olympia Talelli
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