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The Modularity of an Abelian Variety

Axioms
We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over Q.
Jae-Hyun Yang
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SL $$(2,{\mathbb{C}})$$ ( 2 , C ) non-Abelian gauge fields in a photonic molecule array [PDF]

Nature Communications
Engineering the topological properties of the system has been a longstanding subject in physics. Here, we propose a scheme to simulate topological materials with a non-Abelian gauge field in synthetic space-frequency dimensions where the symmetry between
Zhaohui Dong, Xianfeng Chen, Luqi Yuan
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On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties [PDF]

Épijournal de Géométrie Algébrique, 2023
We prove that the rational Chow motive of a six dimensional hyper-K\"{a}hler variety obtained as symplectic resolution of O'Grady type of a singular moduli space of semistable sheaves on an abelian surface $A$ belongs to the tensor category of motives ...
Salvatore Floccari
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Abelian Complex Structures and Generalizations

Complex Manifolds, 2021
After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure.
Poon Yat Sun
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The Abelian Kernel of an Inverse Semigroup

Mathematics, 2020
The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel.
A. Ballester-Bolinches, V. Pérez-Calabuig   +1 more
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$a\times b=c$ in $2+1$D TQFT [PDF]

Quantum, 2021
We study the implications of the anyon fusion equation $a\times b=c$ on global properties of $2+1$D topological quantum field theories (TQFTs). Here $a$ and $b$ are anyons that fuse together to give a unique anyon, $c$.
Matthew Buican, Linfeng Li, Rajath Radhakrishnan   +2 more
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Hopf and Lie algebras in semi-additive Varieties [PDF]

Logical Methods in Computer Science, 2017
We study Hopf monoids in entropic semi-additive varieties with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor.
Hans-E. Porst
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The least dimonoid congruences on relatively free trioids

Математичні Студії, 2022
When Loday and Ronco studied ternary planar trees, they introduced types of algebras, called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associative operations satisfying additional eight axioms relating these ...
A. V. Zhuchok
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Characterization of abelian varieties [PDF]

Inventiones Mathematicae, 2001
10 pages ...
Chen, J.A., Hacon, C.D.
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Logarithmic Abelian Varieties [PDF]

Nagoya Mathematical Journal, 2008
AbstractWe develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.
Kajiwara, Takeshi, Kato, Kazuya, Nakayama, Chikara   +2 more
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