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Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation [PDF]
Communications in Number Theory and Physics, 2020 We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces.
Gálvez Carrillo, Maria Immaculada +2 more
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Revealing topology in metals using experimental protocols inspired by K-theory
Nature Communications, 2023 Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological ...
Wenting Cheng +5 more
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Quarter-BPS states, multi-symmetric functions and set partitions
Journal of High Energy Physics, 2021 We give a construction of general holomorphic quarter BPS operators in N $$ \mathcal{N} $$ = 4 SYM at weak coupling with U(N) gauge group at finite N. The construction employs the Möbius inversion formula for set partitions, applied to multi-symmetric ...
Christopher Lewis-Brown +1 more
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Relative anomaly in (1+1)d rational conformal field theory
Physical Review Research, 2020 We study 't Hooft anomalies of symmetry-enriched rational conformal field theories (RCFT) in (1+1)d. Such anomalies determine whether a theory can be realized in a truly (1+1)d system with on-site symmetry, or on the edge of a (2+1)d symmetry-protected ...
Meng Cheng, Dominic J. Williamson
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8d gauge anomalies and the topological Green-Schwarz mechanism
Journal of High Energy Physics, 2017 String theory provides us with 8d supersymmetric gauge theory with gauge algebras suN,so2N,spN,e6,e7ande8 $$ \mathfrak{s}\mathfrak{u}(N),\mathfrak{s}\mathfrak{o}(2N),\mathfrak{s}\mathfrak{p}(N),{\mathfrak{e}}_6,{\mathfrak{e}}_7\kern0.5em \mathrm{and ...
Iñaki García-Etxebarria +4 more
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Algebras with actions and automata
International Journal of Mathematics and Mathematical Sciences, 1982 In the present paper we want to give a common structure theory of left action, group operations, R-modules and automata of different types defined over various kinds of carrier objects: sets, graphs, presheaves, sheaves, topological spaces (in particular:
W. Kühnel +3 more
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Journal of High Energy PhysicsCluster states are crucial resources for measurement-based quantum computation (MBQC). It exhibits symmetry-protected topological (SPT) order, thus also playing a crucial role in studying topological phases.
Zhian Jia
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PRX QuantumWe present a general framework for constructing quantum cellular automata (QCAs) from topological quantum field theories (TQFTs) and invertible subalgebras (ISAs) using the cup-product formalism.
Meng Sun (孙萌) +4 more
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The Algebraic Topology of Learnability: Bridging PAC Theory to Deep Network Generalization
Deep learning models have achieved remarkable success across various domains, yet a comprehensive theoretical understanding of their generalization capabilities remains an active area of research. Traditional Probably Approximately Correct (PAC) learning theory provides rigorous bounds on generalization errors but often struggles to explain the ...
Revista, Zen, MATH, 10
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Partial Differential Equations in Applied MathematicsThe objective of this study is to calculate the K-Cohomology invariants of certain classification spaces of homotopy groups in short exact sequences, where the computation is done using properties of the K-theoretical features. For these packages we use various applications including K-theory Algebra, which transformed the theory of operator algebra ...
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