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Abelian varieties over finite fields as basic abelian varieties [PDF]
Forum Mathematicum, 2016 In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field.
Yu, Chia-Fu
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Pseudo-abelian varieties [PDF]
Annales scientifiques de l'École normale supérieure, 2013 Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect.
Totaro, Burt
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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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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 +2 more
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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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$a\times b=c$ 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 +2 more
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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 +1 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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Transposition Regular AG-Groupoids and Their Decomposition Theorems
Mathematics, 2022 In this paper, we introduce transposition regularity into AG-groupoids, and a variety of transposition regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties and structures are discussed by their decomposition theorems: (1)
Yudan Du, Xiaohong Zhang, Xiaogang An
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