48 papers
This paper introduces formal multiparameter quantum universal enveloping algebras (FoMpQUEA) as a generalization of Drinfeld's quantum groups, demonstrating that they are closed under toral twists and 2-cocycle deformations, establish a bijective correspondence with multiparameter Lie bialgebras via quantization and semiclassical limits, and prove that specialization and deformation processes commute.
This paper presents a complete classification of complex unital 3-dimensional structurable algebras into seven non-isomorphic classes, detailing their structural properties such as derivation algebras and automorphism groups, and investigates the resulting -graded Lie algebras via the Allison-Kantor construction.
This paper presents a formalization in Lean of the foundational commutative algebra result that projectivity of an -module descends along a faithfully flat ring map, thereby verifying Perry's correction to a subtle gap in the classical work of Raynaud and Gruson.
This paper completes the classification of Nottingham algebras by establishing existence and uniqueness results that determine all such infinite-dimensional, positively graded thin algebras up to isomorphism.
This paper demonstrates that the axioms defining various hypercompositional structures, such as hypergroups and hyperfields, are not independent, and consequently proposes new, minimized definitions that reduce the necessary set of axioms.
This paper characterizes stable equivalences between centralizer matrix algebras over arbitrary fields using a new matrix equivalence relation, demonstrating that such equivalences induce Morita-type stable equivalences that preserve key homological dimensions and validate the Alperin–Auslander/Auslander–Reiten conjecture in this context.
This paper further investigates the function used to construct a canonical connected fundamental domain for , establishing identities to match its cusps with known classes and detailing the domain's boundary arcs and gluing patterns to aid in understanding the modular curve .
This paper develops a theory of quantum cellular automata over arbitrary commutative rings and uses algebraic K-theory to construct a spectrum that classifies these automata up to quantum circuits and stabilization, revealing a deep connection between their classification on Euclidean lattices and the K-theory of Azumaya algebras.