Papers by Ricardo J Franquiz Flores
arXiv (Cornell University), May 23, 2021
We develop the local-global theory of blocks for profinite groups. Given a field k of characteris... more We develop the local-global theory of blocks for profinite groups. Given a field k of characteristic p and a profinite group G, one may express the completed group algebra krrGss as a product ś iPI B i of closed indecomposable algebras, called the blocks of G. To each block B of G we associate a pro-p subgroup of G, called the defect group of B, unique up to conjugacy in G. We give several characterizations of the defect group in analogy with defect groups of blocks of finite groups. Our main theorem is a version of Brauer's first main theorem: a correspondence between the blocks of G with defect group D and the blocks of the normalizer N G pDq with defect group D.
Bulletin of the London Mathematical Society
We demonstrate that the blocks of a profinite group whose defect groups are cyclic have a Brauer ... more We demonstrate that the blocks of a profinite group whose defect groups are cyclic have a Brauer tree algebra structure analogous to the case of finite groups. We show further that the Brauer tree of a block with defect group Zp is of star type.
We develop the local-global theory of blocks for profinite groups. Given a field k of characteris... more We develop the local-global theory of blocks for profinite groups. Given a field k of characteristic p and a profinite group G, one may express the completed group algebra krrGss as a product ś iPI Bi of closed indecomposable algebras, called the blocks of G. To each block B of G we associate a pro-p subgroup of G, called the defect group of B, unique up to conjugacy in G. We give several characterizations of the defect group in analogy with defect groups of blocks of finite groups. Our main theorem is a Brauer correspondence between the blocks of G with defect group D and the blocks of the normalizer NGpDq with defect group D.
Advances in Mathematics
We develop the local-global theory of blocks for profinite groups. Given a field k of characteris... more We develop the local-global theory of blocks for profinite groups. Given a field k of characteristic p and a profinite group G, one may express the completed group algebra krrGss as a product ś iPI B i of closed indecomposable algebras, called the blocks of G. To each block B of G we associate a prop subgroup of G, called the defect group of B, unique up to conjugacy in G. We give several characterizations of the defect group in analogy with defect groups of blocks of finite groups. Our main theorem is a version of Brauer's first main theorem: a correspondence between the blocks of G with defect group D and the blocks of the normalizer N G pDq with defect group D.
A Modified Dirac Operator in Parameter–Dependent Clifford Algebra: A Physical Realization
Advances in Applied Clifford Algebras, 2014
ABSTRACT In the present paper we introduce a modified Dirac operator and solve the associated Dir... more ABSTRACT In the present paper we introduce a modified Dirac operator and solve the associated Dirichlet boundary value problem in $\({\mathbb{R}^3}\)$ for functions which are q–monogenic when the Clifford algebra depends on parameters. By determining the compatibility conditions we establish theorems of existence and uniqueness of solutions to the modified Dirac equation, and the associated Laplace equation, such that they correspond to a scalar operator. We also discuss the problem using fixedpoint methods and analyze a physical realization were the solutions to the Laplace equation can be interpreted as a set of electric potentials coupled to each other. Our solutions could be relevant in the analysis of new exotic phases of nature, such as topological insulators were the Dirac nature of the charge carriers implies new physical properties which go beyond the standard description of conventional charge carriers in electronic systems by means of the Schrödinger equation.
En el 2003 Jesper, Leal y Paques encontraron, para $G$ un grupo finito nilpotente, una técnica al... more En el 2003 Jesper, Leal y Paques encontraron, para $G$ un grupo finito nilpotente, una técnica alternativa a la forma clásica para calcular los idempotentes centrales primitivos de $\mathbb{Q}G$ a partir de parejas de subgrupos de $G$ con ciertas propiedades. Luego en 2004 Olivieri, del Río y Simón cambiaron las condiciones sobre las parejas de subgrupos, ampliando el alcance a la clase de los grupos finitos monomiales que contiene a todos los grupos nilpotentes. Aunque este último resultado es m\'as general, no se conocía si las parejas que satisfacen las condiciones de cumplen las dadas. En este trabajo se realiza un estudio comparativo y se exhibirá ejemplos, de parejas que satisfacen el resultado de Jesper, Leal y Paques pero no el segundo resultado, calculados con un algoritmo creado en el software G.A.P y paquete Wedderga.
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Papers by Ricardo J Franquiz Flores