scholarly journals Orbifolding Frobenius Algebras

2003 ◽  
Vol 14 (06) ◽  
pp. 573-617 ◽  
Author(s):  
Ralph M. Kaufmann
Keyword(s):  
General Theory ◽  
Gauge Group ◽  
Physical Theory ◽  
Group Actions ◽  
Vector Spaces ◽  
Algebraic Structures ◽  
Jacobian Ideal ◽  
Frobenius Algebras

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e. orbifold theories. In this context, we introduce and axiomatize these algebras. Furthermore, we define geometric cobordism categories whose functors to the category of vector spaces are parameterized by these algebras. The theory is also extended to the graded and super-graded cases. As an application, we consider Frobenius algebras having some additional properties making them more tractable. These properties are present in Frobenius algebras arising as quotients of Jacobian ideal, such as those having their origin in quasi-homogeneous singularities and their symmetries.

scholarly journals Frobenius algebras of corepresentations and group-graded vector spaces

2014 ◽  
Vol 406 ◽  
pp. 226-250 ◽  
Author(s):  
S. Dăscălescu ◽  
C. Năstăsescu ◽  
L. Năstăsescu
Keyword(s):  
Vector Spaces ◽  
Frobenius Algebras

The speed of the slow component of ocular nystagmus induced by angular acceleration of the head: its experimental determination and application to the physical theory of the cupular mechanism

1953 ◽  
Vol 141 (903) ◽  
pp. 216-230 ◽  
Keyword(s):  
Experimental Data ◽  
General Theory ◽  
Physical Theory ◽  
Slow Component ◽  
Human Subjects ◽  
Angular Acceleration ◽  
Vertical Axis ◽  
Ocular Nystagmus ◽  
Normal Human ◽  
A New Technique

Angular accelerations around the vertical axis, of known magnitude and duration, have been applied in a number of normal human subjects by means of a rotating chair of new design. Theoretical and experimental evidence is advanced in support of Graybiel’s hypothesis that the oculo-gyral illusion is dependent upon vestibular eye nystagmus. A new technique is described for the quantitative evaluation of the oculo-gyral illusion occurring during the application of known angular accelerations. According to the theoretical and experimental data given, this technique makes it possible to obtain instantaneous measurements of the speed of the slow component of such vestibular eye nystagmus occurring at any point in the course of application of known angular accelerations and accordingly of the instantaneous magnitude of the corresponding cupular deflexion. By this means it has been possible to substantiate the general theory of the cupular mechanism outlined by Steinhausen and to re-evaluate and confirm the physical constants of the system assigned to it by Van Egmond and his co-workers.

MULTIPLICITY ONE PROPERTY AND THE DECOMPOSITION OF b-FUNCTIONS

2006 ◽  
Vol 17 (02) ◽  
pp. 195-229 ◽  
Author(s):  
FUMIHIRO SATO ◽  
KAZUNARI SUGIYAMA
Keyword(s):  
Group Actions ◽  
Polynomial Rings ◽  
Vector Spaces ◽  
Prehomogeneous Vector Spaces ◽  
Multiplicity One

Recently, extensive calculations have been made on b-functions of prehomogeneous vector spaces with reducible representations. By examining the results of these calculations, we observe that b-functions of a large number of reducible prehomogeneous vector spaces have decompositions which seem to be correlated to the decomposition of representations. In the present paper, we show that such phenomena can be ascribed to a certain multiplicity one property for group actions on polynomial rings. Furthermore, we give some criteria for the multiplicity one property. Our method can be applied equally to non-regular prehomogeneous vector spaces.

Algebraic Structures II (Vector Spaces and Finite Fields)

2019 ◽  
pp. 191-224
Author(s):  
R. Balakrishnan ◽  
Sriraman Sridharan
Keyword(s):  
Finite Fields ◽  
Vector Spaces ◽  
Algebraic Structures

A general reciprocity law for symbols on arbitrary vector spaces

2018 ◽  
Vol 17 (06) ◽  
pp. 1850101
Author(s):  
Fernando Pablos Romo
Keyword(s):  
General Theory ◽  
General Expression ◽  
Vector Spaces ◽  
Residue Theorem ◽  
Arbitrary Vector ◽  
The Past ◽  
Reciprocity Laws ◽  
Reciprocity Law ◽  
Norm Residue ◽  
Hilbert Norm

The aim of this work is to offer a general theory of reciprocity laws for symbols on arbitrary vector spaces and to show that classical explicit reciprocity laws are particular cases of this theory (sum of valuations on a complete curve, Residue Theorem, Weil Reciprocity Law and the Reciprocity Law for the Hilbert Norm Residue Symbol). Moreover, several reciprocity laws introduced over the past few years by D. V. Osipov, A. N. Parshin, I. Horozov, I. Horozov — M. Kerr and the author — together with D. Hernández Serrano — can also be deduced from this general expression.

Sign in / Sign up

Export Citation Format

Share Document