Results 21 to 30 of about 57 (48)
Topological K‐theory of quasi‐BPS categories for Higgs bundles
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract In a previous paper, we introduced quasi‐BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi‐BPS categories (called BPS in this case) are noncommutative analogues of Hitchin integrable systems.
Tudor Pădurariu, Yukinobu Toda
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Groupoid Graded Semisimple Rings [PDF]
We develop the theory of groupoid graded semisimple rings. Our rings are neither unital nor one-sided artinian. Instead, they exhibit a strong version of having local units and being locally artinian, and we call them $Γ_0$-artinian.
Cristiano, Zaqueu +2 more
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The geometry and arithmetic of bielliptic Picard curves
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
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Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
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Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley [PDF]
, 2010 Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures ...
Lynch, Laura
core
PBW Deformations of Smash Products Involving Hopf Algebra of Kac–Paljutkin Type
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let H2n2 be the Kac–Paljutkin–type Hopf algebra of dimension 2n2, A its graded Koszul Artin–Schelter regular H2n2‐module algebra of Dimension 2, A! the Koszul dual of A, and Acop the braided‐opposite algebra of A. This paper describes (0, 1)‐degree PBW deformations of the smash product A♯H2n2 and those of A!♯H2n2 under the condition that the Koszul ...
Yujie Gao, Shilin Yang, Naihuan Jing
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Reflecting perfection for finite‐dimensional differential graded algebras
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3689-3707, December 2024.Abstract We generalise two facts about finite‐dimensional algebras to finite‐dimensional differential graded algebras. The first is the Nakayama lemma and the second is that the simples can detect finite projective dimension. We prove two dual versions which relate to Gorenstein differential graded algebras and Koszul duality, respectively.
Isambard Goodbody
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L${L}$‐functions of Kloosterman sheaves
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract In this article, we study a family of motives Mn+1k$\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1$n=1$, the L$L$‐functions of M2k$\mathrm{M}_{2}^k$ extend meromorphically to C$\mathbb {C}$ and satisfy the functional equations conjectured by ...
Yichen Qin
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A constructive proof of the Wedderburn-Artin theorem [PDF]
In this paper, we use the idempotent decomposition to give an explicit isomorphism from an arbitrary semisimple Artinian ring to an external direct sum of finitely many full matrix rings over division rings.4 ...
Gao, Sheng
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A functorial approach to monomorphism categories II: Indecomposables
Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.Abstract We investigate the (separated) monomorphism category mono(Q,Λ)$\operatorname{mono}(Q,\Lambda)$ of a quiver over an Artin algebra Λ$\Lambda$. We show that there exists an epivalence (called representation equivalence in the terminology of Auslander) from mono¯(Q,Λ)$\overline{\operatorname{mono}}(Q,\Lambda)$ to rep(Q,mod¯Λ)$\operatorname{rep}(Q,\
Nan Gao +3 more
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