33,444 research outputs found
Auslander correspondence
We study Auslander correspondence from the viewpoint of higher dimensional
Auslander-Reiten theory on maximal orthogonal subcategories. We give
homological characterizations of Auslander algebras, especially an answer to a
question of M. Artin. They are also closely related to Auslander's
representation dimension of artin algebras and Van den Bergh's non-commutative
crepant resolutions of Gorenstein singularities.Comment: 29 pages. Final Version. To appear in Adv. Mat
Generalized binary arrays from quasi-orthogonal cocycles
Generalized perfect binary arrays (GPBAs) were used by Jedwab to
construct perfect binary arrays. A non-trivial GPBA can exist only if its energy
is 2 or a multiple of 4. This paper introduces generalized optimal binary arrays
(GOBAs) with even energy not divisible by 4, as analogs of GPBAs. We give a
procedure to construct GOBAs based on a characterization of the arrays in terms
of 2-cocycles. As a further application, we determine negaperiodic Golay pairs
arising from generalized optimal binary sequences of small length.Junta de Andalucía FQM-01
Relative asymptotics for orthogonal matrix polynomials
In this paper we study sequences of matrix polynomials that satisfy a
non-symmetric recurrence relation. To study this kind of sequences we use a
vector interpretation of the matrix orthogonality. In the context of these
sequences of matrix polynomials we introduce the concept of the generalized
matrix Nevai class and we give the ratio asymptotics between two consecutive
polynomials belonging to this class. We study the generalized matrix Chebyshev
polynomials and we deduce its explicit expression as well as we show some
illustrative examples. The concept of a Dirac delta functional is introduced.
We show how the vector model that includes a Dirac delta functional is a
representation of a discrete Sobolev inner product. It also allows to
reinterpret such perturbations in the usual matrix Nevai class. Finally, the
relative asymptotics between a polynomial in the generalized matrix Nevai class
and a polynomial that is orthogonal to a modification of the corresponding
matrix measure by the addition of a Dirac delta functional is deduced
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