74,200 research outputs found
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities
involving Bessel functions with half-integer orders and other special
functions. These identities appear in the famous Handbook of Mathematical
Functions, as well as in its successor, the DLMF, but their proofs were lost.
We use generating functions and symbolic summation techniques to produce new
proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl
Hopf cyclic cohomology in braided monoidal categories
We extend the formalism of Hopf cyclic cohomology to the context of braided
categories. For a Hopf algebra in a braided monoidal abelian category we
introduce the notion of stable anti-Yetter-Drinfeld module. We associate a
para-cocyclic and a cocyclic object to a braided Hopf algebra endowed with a
braided modular pair in involution in the sense of Connes and Moscovici. When
the braiding is symmetric the full formalism of Hopf cyclic cohomology with
coefficients can be extended to our categorical setting.Comment: 50 pages. One reference added. Proofs are visualized through braiding
diagrams. Final version to appear in `Homology, Homotopy and Applications
Convolution algebras and the deformation theory of infinity-morphisms
Given a coalgebra C over a cooperad, and an algebra A over an operad, it is
often possible to define a natural homotopy Lie algebra structure on hom(C,A),
the space of linear maps between them, called the convolution algebra of C and
A. In the present article, we use convolution algebras to define the
deformation complex for infinity-morphisms of algebras over operads and
coalgebras over cooperads. We also complete the study of the compatibility
between convolution algebras and infinity-morphisms of algebras and coalgebras.
We prove that the convolution algebra bifunctor can be extended to a bifunctor
that accepts infinity-morphisms in both slots and which is well defined up to
homotopy, and we generalize and take a new point of view on some other already
known results. This paper concludes a series of works by the two authors
dealing with the investigation of convolution algebras.Comment: 17 pages, 1 figure; (v2): Expanded some proofs, corrected typos,
updated references. Final versio
Polynomial identity rings as rings of functions
We generalize the usual relationship between irreducible Zariski closed
subsets of the affine space, their defining ideals, coordinate rings, and
function fields, to a non-commutative setting, where "varieties" carry a
PGL_n-action, regular and rational "functions" on them are matrix-valued,
"coordinate rings" are prime polynomial identity algebras, and "function
fields" are central simple algebras of degree n. In particular, a prime
polynomial identity algebra of degree n is finitely generated if and only if it
arises as the "coordinate ring" of a "variety" in this setting. For n = 1 our
definitions and results reduce to those of classical affine algebraic geometry.Comment: 24 pages. This is the final version of the article, to appear in J.
Algebra. Several proofs have been streamlined, and a new section on
Brauer-Severi varieties has been adde
Galois cohomology of a number field is Koszul
We prove that the Milnor ring of any (one-dimensional) local or global field
K modulo a prime number l is a Koszul algebra over Z/l. Under mild assumptions
that are only needed in the case l=2, we also prove various module Koszulity
properties of this algebra. This provides evidence in support of Koszulity
conjectures that were proposed in our previous papers. The proofs are based on
the Class Field Theory and computations with quadratic commutative Groebner
bases (commutative PBW-bases).Comment: LaTeX 2e, 25 pages; v.2: minor grammatic changes; v.3: classical
references added, remark inserted in subsection 1.6, details of arguments
added in subsections 1.4, 1.7 and sections 5 and 6; v.4: still more misprints
corrected, acknowledgement updated, a sentence inserted in section 4, a
reference added -- this is intended as the final versio
Tate (co)homology via pinched complexes
For complexes of modules we study two new constructions, which we call the
pinched tensor product and the pinched Hom. They provide new methods for
computing Tate homology and Tate cohomology, which lead to conceptual proofs of
balancedness of Tate (co)homology for modules over associative rings.
Another application we consider is in local algebra. Under conditions of
vanishing of Tate (co)homology, the pinched tensor product of two minimal
complete resolutions yields a minimal complete resolution.Comment: Final version; 23 pp. To appear in Trans. Amer. Math. So
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