48 papers
This paper investigates the complex reflection group associated with the octahedral group by determining its irreducible representations and character table, computing the modules of vector-valued invariants for each representation, and deriving explicit dimension formulas for the corresponding rings of invariants.
This paper provides proofs for Miyashita's characterizations of separable and Hirata separable polynomials in the general skew polynomial ring , extending the author's previous elementary proofs from the specific automorphism and derivation cases.
This paper characterizes -matching, interchangeable, and totally compatible products specifically within the context of null-filiform associative algebras.
This paper provides a comprehensive survey of various Waring-type problems across the mathematical structures of groups, Lie algebras, and associative algebras.
This paper constructs new cotorsion pairs in an abelian category by gluing cotorsion pairs from a recollement's outer components, establishes conditions for their coincidence and completeness, and applies these results to Morita rings while introducing a specific class of recollements with enhanced homological properties.
This paper introduces the concept of balanced matrices, investigating their properties under matrix operations and demonstrating that for $2\times 2$ balanced matrices, the leading entry, trace, determinant, and eigenvalues are directly linked, enabling the prediction of quadratic forms solely from the spectrum.
This paper establishes that an affine transformation in is a product of two coninvolutions if and only if its linear part is -reversible, while also characterizing products of three coninvolutions and proving that every transformation with a linear part of unit determinant is a product of at most four coninvolutions.
This paper classifies three-dimensional associative algebras over arbitrary base fields of characteristic different from two and three by providing canonical representatives for their isomorphism classes and comparing these results with existing classifications over complex numbers and for the nilpotent case.
This paper extends the complex multipoint Schwarz-Pick Lemma to the quaternionic setting of slice regular functions using iterated hyperbolic difference quotients, thereby deriving new estimates and providing an algorithm for constructing interpolating functions with real nodes.
This paper determines the unique birationally rigid induction datum for every -equivariant nilpotent cover of a nilpotent coadjoint orbit in a semisimple simply connected algebraic group of exceptional type over .
This paper determines all -biderivations for the Witt algebra, the Virasoro algebra, the -algebras , and their universal central extensions , and subsequently presents applications of these results.
This paper generalizes and improves upon Hamaguchi and Nakajima's work by characterizing weakly separable polynomials over commutative rings using derivatives and discriminants, while also establishing necessary and sufficient conditions for such polynomials in noncommutative skew polynomial rings.
This paper characterizes weakly separable polynomials in skew polynomial rings and explores the relationship between separability and weak separability in rings of derivation type, building upon the generalization of separable extensions introduced by Hamaguchi and Nakajima.
This paper establishes the Morita invariance of several classes of ring extensions and provides a counterexample of a class that is not Morita invariant, building upon previous results by Miyashita and Ikehata.
This paper extends known results on nonmatrix varieties of associative algebras from the case of infinite fields to the more general setting of unital commutative rings, specifically characterizing varieties of -algebras that do not contain the algebra of matrices.
This paper establishes a Knebusch-type trace formula for signatures of hermitian forms over Azumaya algebras with involution, extending Knebusch's results on symmetric bilinear forms and yielding an exact sequence for total signatures over semilocal base rings that relates to Pfister's local-global principle and the stability index.
Inspired by the work of Enriquez and Furusho, this paper provides a stabilizer interpretation for both the linearized double shuffle Lie algebra and its extension accommodating multiple q-zeta values and multiple Eisenstein series, demonstrating that these stabilizers preserve the extension between the two algebras.
This paper constructs a mutation cone and a corresponding wall-and-chamber structure for maximal modifying modules over 3-dimensional Gorenstein isolated singularities, proving that the tilting-noetherian property holds if and only if all such modules are mutation-connected, and establishing a regular covering map from a specific subspace of Bridgeland stability conditions to the complexified mutation cone to describe the associated autoequivalence group.
This paper introduces one-sided --Gorenstein categories as a generalization of Gorenstein categories, establishes equivalent characterizations based on relative projective and injective dimensions, and derives a necessary condition for the validity of the Wakamatsu tilting conjecture.
This paper introduces Calabi--Yau quadruples to demonstrate that their associated Higgs categories are -Calabi--Yau Frobenius extriangulated categories with canonical -cluster-tilting subcategories, thereby proving that both relative Amiot--Guo--Keller and Higgs constructions transform silting reduction into Calabi--Yau reduction.