Books by Blas Torrecillas
Papers by Blas Torrecillas
We present a rich source of Hopf algebras starting from a cofinite central extension of a Noether... more We present a rich source of Hopf algebras starting from a cofinite central extension of a Noetherian Hopf algebra and a subgroup of the algebraic group of characters of the central Hopf subalgebra. The construction is transparent from a Tannakian perspective. We determine when the new Hopf algebras are co-Frobenius, or cosemisimple, or Noetherian, or regular, or have finite Gelfand-Kirillov dimension.
Información del artículo Condiciones de finitud y módulos T-inyectivos.
Extracta mathematicae, 1991
EXTRACTA MATHEMATICAE Vol. 6, Núm. 1, 12-14 (1991) Quasi-Frobenius Quotient Rings * J. GÓMEZ TORR... more EXTRACTA MATHEMATICAE Vol. 6, Núm. 1, 12-14 (1991) Quasi-Frobenius Quotient Rings * J. GÓMEZ TORRECILLAS, BLAS TORRECILLAS JOVER Fac. Ciencias, Campus Almería, Univ. Granada, 04071 Almería, Spain AMS Subject Class. (1980): 16A08, 16A36, 16A63 ...
AIMS mathematics, 2022
Framework and justification: The content of this paper is located on the intersection of two fiel... more Framework and justification: The content of this paper is located on the intersection of two fields: Finance and Algebra. In effect, the current dynamism shown by most financial instruments makes it necessary to endow the foundations of finance with, as general as possible, algebraic structures. Therefore, the objective of this paper is to provide a novel view of the fundamentals of finance by using purely algebraic concepts and structures, more specifically the properties of separability and additivity of the involved discount functions and their corresponding operators. This approach provides more flexibility to the axioms of financial mathematics, so anticipating potential changes in the behavior of the so-called "rational" decision makers. Methodologically, this paper uses a variety of algebraic tools which fit the intuition behind the financial logic. Indeed, the main contribution of the paper is the wide variety of algebraic concepts belonging to the abstract algebra which can be applied to describe the behavior of intertemporal choices.
Springer eBooks, 1988
Resumen The papers in this proceedings volume are selected research papers in different areas of ... more Resumen The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology ...
arXiv (Cornell University), Sep 10, 2012
For a finite cyclic p-group G and a discrete valuation domain R of characteristic 0 with maximal ... more For a finite cyclic p-group G and a discrete valuation domain R of characteristic 0 with maximal ideal pR the R[G]-permutation modules are characterized in terms of the vanishing of first degree cohomology on all subgroups (cf. Thm. A). As a consequence any R[G]-lattice can be presented by R[G]-permutation modules (cf. Thm. C). The proof of these results is based on a detailed analysis of the category of cohomological G-Mackey functors with values in the category of R-modules. It is shown that this category has global dimension 3 (cf. Thm. E). A crucial step in the proof of Theorem E is the fact that a gentle R-order category (with parameter p) has global dimension less or equal to 2 (cf. Thm. D).
Colloquium Mathematicum, 2020
Journal of Pure and Applied Algebra, Dec 1, 2019
We classify the monoidal structures for the category of N-complexes which respect the graded stru... more We classify the monoidal structures for the category of N-complexes which respect the graded structure.
In this paper we introduce the notion of rooted ring with several objects (rooted small preadditi... more In this paper we introduce the notion of rooted ring with several objects (rooted small preadditive category). Then, we obtain characterizations of projective and flat functors in the corresponding functor category, and use them to give new results concerning right perfect rooted rings with several objects and pure semisimple finitely presented additive categories. We conclude the paper applying the results to the module category over a rooted ring with enough idempotents.
arXiv (Cornell University), Mar 24, 2023
We present a rich source of Hopf algebras starting from a cofinite central extension of a Noether... more We present a rich source of Hopf algebras starting from a cofinite central extension of a Noetherian Hopf algebra and a subgroup of the algebraic group of characters of the central Hopf subalgebra. The construction is transparent from a Tannakian perspective. We determine when the new Hopf algebras are co-Frobenius, or cosemisimple, or Noetherian, or regular, or have finite Gelfand-Kirillov dimension. 2020 Mathematics Subject Classification. 16T05; 18M05. Notations. The natural numbers are denoted by N, and N 0 = N ∪ {0}. Given m < n ∈ N 0 , we set I m,n = {i ∈ N 0 : m ≤ i ≤ m} and I n = I 1,n. 'Algebra' means associative unital algebra. The space of algebra homomorphism from a k-algebra A to a k-algebra B is denoted by Alg(A, B). The category of finite-dimensional left R-modules, where R is an algebra, is denoted by rep R. All Hopf algebras are supposed to have bijective antipode. We write M ≤ N to express that M is a subobject of N in a given category.
CRC Press eBooks, May 8, 2001
Journal of Algebra, Oct 1, 1995
Contemporary mathematics, 2021
Memoirs of the American Mathematical Society, Mar 1, 2021
Journal of Algebra, Feb 1, 1987
Unified products and split extensions of Hopf algebras by A. L. Agore and G. Militaru Hopf monoid... more Unified products and split extensions of Hopf algebras by A. L. Agore and G. Militaru Hopf monoids in the category of species by M. Aguiar and S. Mahajan Classifying Hopf algebras of a given dimension by M. Beattie and G. A. Garcia On the double crossed product of weak Hopf algebras by G. Bohm and J. Gomez-Torrecillas The doubles of a braided Hopf algebra by A. Bruguieres and A. Virelizier Induced conjugacy classes and induced ${\mathcal U}_{\varepsilon}(G)$-modules by G. Carnovale Recovering information from character tables of Hopf algebras: Normality, dimensions and quotients by M. Cohen and S. Westreich Hom-quasi-bialgebras by M. Elhamdadi and A. Makhlouf On twisted conjugacy classes of type D in sporadic simple groups by F. Fantino and L. Vendramin Partial and unified crossed products are weak crossed products by J. M. F. Vilaboa, R. G. Rodriguez, and A. B. R. Raposo The Green rings of the generalized Taft Hopf algebras by L. Li and Y. Zhang Morita equivalence methods in classification of fusion categories by D. Nikshych
arXiv (Cornell University), Oct 20, 2020
This paper is the first part of a series devoted to the study of the quadratic algebras with rela... more This paper is the first part of a series devoted to the study of the quadratic algebras with relations generated by superpotentials which are exterior 3-forms. Such an algebra is regular if and only if it is Koszul and is then a 3-Calabi-Yau domain. After some general results we investigate the case of the algebras generated in low dimensions n with n ≤ 7. We show that whenever the ground field is algebraically closed all these algebras associated with 3-regular exterior 3-forms are regular and are thus 3-Calabi-Yau domains.
arXiv (Cornell University), Oct 11, 2011
We prove that a profinite algebra whose left (right) cyclic modules are torsionless is finite dim... more We prove that a profinite algebra whose left (right) cyclic modules are torsionless is finite dimensional and QF. We give a relative version of the notion of left (right) PF ring for pseudocompact algebras and prove it is left-right symmetric and dual to the notion of quasi-co-Frobenius coalgebras. We also prove two ring theoretic conjectures of Faith, in the setting (and supplementary hypothesis) of profinite algebras: any profinite semiartinian selfinjective algebra is finite dimensional and QF, and any FGF profinite algebra is finite dimensional QF.
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Books by Blas Torrecillas
Papers by Blas Torrecillas