Search results for "Mathematics::Commutative Algebra"
showing 10 items of 90 documents
Unbounded C$^*$-seminorms and $*$-Representations of Partial *-Algebras
2009
The main purpose of this paper is to construct *-representations from unbounded C*-seminorms on partial *-algebras and to investigate their *-representations. © Heldermann Verlag.
Multiple Points in the Target: The Case of Parameterised Hypersurfaces
2020
We focus on parameterised hypersurfaces, and explore the information one can obtain from the matrix of a presentation of the push-forward of the structure sheaf, through the use of Fitting ideals. We show that in a number of cases the spaces defined by the Fitting ideals are Cohen–Macaulay, extending the previously known range. We prove the Milnor–Tjurina relation for parameterised hypersurfaces whose dimension is no greater than two.
Specht property for some varieties of Jordan algebras of almost polynomial growth
2019
Abstract Let F be a field of characteristic zero. In [25] it was proved that U J 2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z 2 -gradings or by a Z 2 × Z 2 -grading. In this paper we prove that the variety of Jordan algebras generated by U J 2 endowed with any G-grading has the Specht property, i.e., every T G -ideal containing the graded identities of U J 2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A 1 , a suitable infinitely generated metabelian Jordan algebra defined in [27] .
Graded polynomial identities and exponential growth
2009
Let $A$ be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group $G$. Here we study a growth function related to the graded polynomial identities satisfied by $A$ by computing the exponential rate of growth of the sequence of graded codimensions of $A$. We prove that the $G$-exponent of $A$ exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of $A$.
Truncated modules and linear presentations of vector bundles
2018
We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method allows one to produce several new examples, and provides an alternative point of view on the existing ones.
On multiplicities of cocharacters for algebras with superinvolution
2021
Abstract In this paper we deal with finitely generated superalgebras with superinvolution, satisfying a non-trivial identity, whose multiplicities of the cocharacters are bounded by a constant. Along the way, we prove that the codimension sequence of such algebras is polynomially bounded if and only if their colength sequence is bounded by a constant.
Cox ring of the generic fiber
2017
Abstract Given a surjective morphism π : X → Y of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of π from the Cox ring of X. As a corollary we show that in some cases it is also possible to recover the Cox ring of a very general fiber, and finally we give an application in the case of the blowing-up of a toric fiber space.
Crystal structure of 5′′-(4-chlorobenzylidene)-4′-(4-chlorophenyl)-1′-methyltrispiro[acenapthylene-1,2′-pyrrolidine-3′,1′′-cyclohexane-3′′,2′′′-[1,3]…
2015
In the title compound, C36H29Cl2NO4, two spiro links connect the methyl-substituted pyrrolidine ring to the acenaphthylene and cyclohexanone rings. The cyclohexanone ring is further connected to the dioxalane ring by a third spiro junction. The five-membered ring of the acenaphthylen-1-one ring system adopts a flattened envelope conformation, with the ketonic C atom as the flap, whereas the dioxalane and pyrrolidine rings each have a twist conformation. The cyclohexenone ring assumes a boat conformation. An intramolecular C—H...O hydrogen-bond interaction is present. In the crystal, molecules are linked by non-classical C—H...O hydrogen bonds, forming chains extending parallel to theaaxis.
Graded metrics adapted to splittings
1997
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul, are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry: It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion an…
Algebras with intermediate growth of the codimensions
2006
AbstractLet F be a field of characteristic zero and let A be an F-algebra. The polynomial identities satisfied by A can be measured through the asymptotic behavior of the sequence of codimensions and the sequence of colengths of A. For finite dimensional algebras we show that the colength sequence of A is polynomially bounded and the codimension sequence cannot have intermediate growth. We then prove that for general nonassociative algebras intermediate growth of the codimensions is allowed. In fact, for any real number 0<β<1, we construct an algebra A whose sequence of codimensions grows like nnβ.