Journal ArticleDOI
The algebraic structure of linearly recursive sequences under hadamard product
Richard G. Larson,Earl J. Taft +1 more
TLDR
In this article, the algebraic structure of linearly recursive sequences under the Hadamard product was described and the invertible elements and zero divisors were characterized using Hopf algebras.Abstract:
We describe the algebraic structure of linearly recursive sequences under the Hadamard (point-wise) product. We characterize the invertible elements and the zero divisors. Our methods use the Hopf-algebraic structure of this algebra and classical results on Hopf algebras. We show that our criterion for invertibility is effective if one knows a linearly recursive relation for a sequence and certain information about finitely-generated subgroups of the multiplicitive group of the field.read more
Citations
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Journal ArticleDOI
Witt and Virasoro algebras as lie bialgebras
Earl J. Taft,Earl J. Taft +1 more
TL;DR: In this article, a countably infinite number of Lie coalgebra structures on the Witt algebra W = Der k [ x ] over a field k, and on the Virasoro algebras W 1 =Der k [x, x −1 ] and V = W 1 ⊕ kc with central charge c.
Journal ArticleDOI
Generalizing Zeckendorf's Theorem to f-decompositions
TL;DR: In this article, it was shown that every positive integer can be uniquely decomposed as a sum of non-consecutive Fibonacci numbers, where F 1 = 1, F 2 = 2 and F n+1 = F n + F n − 1.
Book ChapterDOI
Solving Linear Recurrence Equations with Polynomial Coefficients
Marko Petkovšek,Helena Zakrajšek +1 more
TL;DR: In this paper, the problem of finding polynomial, rational, hypergeometric, d'Alembertian, and Liouvillian solutions of linear recurrences is studied.
Posted Content
Universal construction of topological theories in two dimensions
TL;DR: In this paper, Blanchet, Habegger, Masbaum and Vogel's universal construction of topological theories in dimension two is considered, using it to produce interesting theories that do not satisfy the usual two-dimensional TQFT axioms.
Journal ArticleDOI
Functorial constructions for non-associative algebras with applications to quasi-bialgebras
TL;DR: In this paper, the authors establish a contravariant adjunction between the category of quasi-bialgebras and a suitable full subcategory of dual quasi-biels, adapting the notion of finite dual to this framework.
References
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Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures:
Book
Representation Theory of Finite Groups and Associative Algebras
Charles W. Curtis,Irving Reiner +1 more
TL;DR: In this paper, the authors present a group theory representation and modular representation for algebraic number theory, including Semi-Semi-Simple Rings and Group Algebras, including Frobenius Algebraic numbers.
Book
Number theory and applications
TL;DR: In this paper, the authors present the results of the 1988 NATO Advanced Study Institute (NASI) conference on the "NATO Advanced Study Program" (NAPP).
Journal ArticleDOI
The hopf algebra of linearly recursive sequences
Brian Peterson,Earl J. Taft +1 more
TL;DR: In this article, the authors considered the space of linearly recursive sequences over a field can be considered as a Hopf algebra and gave an algorithm for diagonalizing a sequence in terms of the basis of the coalgebra it generates formed by its images under the difference-operator shift.