346 research outputs found
Strict polynomial functors and coherent functors
We build an explicit link between coherent functors in the sense of Auslander
and strict polynomial functors in the sense of Friedlander and Suslin.
Applications to functor cohomology are discussed.Comment: published version, 24 pages. Section 2.7 reorganized, and notational
distinction between left and right tensor product reinstalle
Theta functions on the Kodaira-Thurston manifold
We define analogue of theta-functions on the Kodaira--Thurston manifold which
is a compact 4-dimensional symplectic manifold and use them to construct
canonical symplectic embedding of the Kodaira--Thurston manifold into the
complex projective space (analogue of the Lefshetz theorem).Comment: 11 page
A faster pseudo-primality test
We propose a pseudo-primality test using cyclic extensions of . For every positive integer , this test achieves the
security of Miller-Rabin tests at the cost of Miller-Rabin
tests.Comment: Published in Rendiconti del Circolo Matematico di Palermo Journal,
Springe
Algebraic K-theory of endomorphism rings
We establish formulas for computation of the higher algebraic -groups of
the endomorphism rings of objects linked by a morphism in an additive category.
Let be an additive category, and let Y\ra X be a covariant
morphism of objects in . Then for all , where is the
quotient ring of the endomorphism ring of modulo the
ideal generated by all those endomorphisms of which factorize through .
Moreover, let be a ring with identity, and let be an idempotent element
in . If is homological and has a finite projective resolution
by finitely generated projective -modules, then for all . This reduces calculations of the higher
algebraic -groups of to those of the quotient ring and the corner
ring , and can be applied to a large variety of rings: Standardly
stratified rings, hereditary orders, affine cellular algebras and extended
affine Hecke algebras of type .Comment: 21 pages. Representation-theoretic methods are used to study the
algebraic K-theory of ring
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
Evaluating Matrix Circuits
The circuit evaluation problem (also known as the compressed word problem)
for finitely generated linear groups is studied. The best upper bound for this
problem is , which is shown by a reduction to polynomial
identity testing. Conversely, the compressed word problem for the linear group
is equivalent to polynomial identity testing. In
the paper, it is shown that the compressed word problem for every finitely
generated nilpotent group is in . Within
the larger class of polycyclic groups we find examples where the compressed
word problem is at least as hard as polynomial identity testing for skew
arithmetic circuits
Abstract Poisson summation formulas over homogeneous spaces of compact groups
This paper presents the abstract notion of Poisson summation formulas for homogeneous spaces of compact groups. Let G be a compact group, H be a closed subgroup of G, and μ be the normalized G-invariant measure over the left coset space G / H associated to the Weil’s formula. We prove that the abstract Fourier transform over G / H satisfies a generalized version of the Poisson summation formula
Pollution-Affected Fish Hepatic Transcriptome and Its Expression Patterns on Exposure to Cadmium
Individuals of the fish Lithognathus mormyrus were exposed to a series of pollutants including: benzo[a]pyrene, pp-DDE, Aroclor 1254, perfluorooctanoic acid, tributyl-tin chloride, lindane, estradiol, 4-nonylphenol, methyl mercury chloride, and cadmium chloride. Five mixtures of the pollutants were injected. Each mixture included one to three compounds. A microarray was constructed using 4608 L. mormyrus hepatic cDNAs cloned from the pollutant-exposed fish. Most clones (4456) were sequenced and assembled into 1494 annotated unique clones. The constructed microarray was used to identify changes in hepatic gene expression profile on exposure to cadmium administered to the fish by feeding or injections. Thirty-one unique clones showed altered expression levels on exposure to cadmium. Prominently differentially expressed genes included elastase 4, carboxypeptidase B, trypsinogen, perforin, complement C31, cytochrome P450 2K5, ceruloplasmin, carboxyl ester lipase, and metallothionein. Twelve sequences have no available annotation. Most genes (23) were downregulated and hypothesized to be affected by general toxicity due to the intensive cadmium exposure regime. The concept of an operational multigene cDNA microarray, aimed at routine and fast biomonitoring of multiple environmental threats, is outlined and the cadmium exposure experiment has been used to demonstrate functional and methodological aspects of the biomonitoring tool. The components of the outlined system include: (1) spotted array, composed of both pollution-affected and constitutively expressed genes, the latter are used for normalization; (2) standard, repeatable labeling procedure of a reference transcript population; and (3) biomarker indices derived from the profile of expression ratio across the pollution-affected genes, between the field-sampled transcript populations and the reference
On quiver Grassmannians and orbit closures for representation-finite algebras
We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation- nite algebra, we use the projective quotient algebra to construct desingularizations of quiver Grassmannians, orbit closures in representation varieties, and their desingularizations. This generalizes results of Cerulli Irelli, Feigin and Reineke
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