A classification of irreducible prehomogeneous vector spaces over an algebraically closed field of characteristic 2 (I)

1986 ◽  
Vol 2 (2) ◽  
pp. 168-177 ◽  
Author(s):  
Chen Zhijie
Keyword(s):  
Vector Spaces ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Prehomogeneous Vector Spaces ◽  
Characteristic 2

scholarly journals Classification of one-dimensional superattracting germs in positive characteristic

2014 ◽  
Vol 35 (7) ◽  
pp. 2242-2268 ◽  
Author(s):  
MATTEO RUGGIERO
Keyword(s):  
Positive Characteristic ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Dimensional Version

We give a classification of superattracting germs in dimension $1$ over a complete normed algebraically closed field $\mathbb{K}$ of positive characteristic up to conjugacy. In particular, we show that formal and analytic classifications coincide for these germs. We also give a higher-dimensional version of some of these results.

scholarly journals A classification of 3-simple prehomogeneous vector spaces of nontrivial type

1996 ◽  
Vol 22 (1) ◽  
pp. 159-198 ◽  
Author(s):  
Tatsuo KIMURA ◽  
Kosei UEDA ◽  
Takeshi YOSHIGAKI
Keyword(s):  
Vector Spaces ◽  
Prehomogeneous Vector Spaces

Pencils of real binary cubics

1983 ◽  
Vol 93 (3) ◽  
pp. 477-484 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Real Case ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
The Real

A complete and satisfying account of the classification of pencils of binary cubics over an algebraically closed field was given by Newstead (2). Extending these results to the real case is not a matter of mere routine since new questions arise, for example the separation of roots of the cubics in a pencil (as well as their reality).

HOPF ALGEBRAS OF DIMENSION 30

2010 ◽  
Vol 09 (01) ◽  
pp. 11-15 ◽  
Author(s):  
DAIJIRO FUKUDA
Keyword(s):  
Hopf Algebra ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Finite Dimensional

This paper contributes to the classification of finite dimensional Hopf algebras. It is shown that every Hopf algebra of dimension 30 over an algebraically closed field of characteristic zero is semisimple and thus isomorphic to a group algebra or the dual of a group algebra.

scholarly journals Multiplicities in the Tensor Product of Finite-Dimensional Representations of Discrete Groups

1978 ◽  
Vol 21 (1) ◽  
pp. 17-19
Author(s):  
Dragomir Ž. Djoković
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Unitary Representations ◽  
Vector Spaces ◽  
Closed Field ◽  
Discrete Groups ◽  
Algebraically Closed Field ◽  
Finite Dimensional ◽  
Irreducible Unitary Representations

Let G be a group and ρ and σ two irreducible unitary representations of G in complex Hilbert spaces and assume that dimp ρ= n < ∞. D. Poguntke [2] proved that is a sum of at most n2 irreducible subrepresentations. The case when dim a is also finite he attributed to R. Howe.We shall prove analogous results for arbitrary finite-dimensional representations, not necessarily unitary. Thus let F be an algebraically closed field of characteristic 0. We shall use the language of modules and we postulate that allour modules are finite-dimensional as F-vector spaces. The field F itself will be considered as a trivial G-module.

scholarly journals A classification of 2-simple prehomogeneous vector spaces of type I

1988 ◽  
Vol 114 (2) ◽  
pp. 369-400 ◽  
Author(s):  
Tatsuo Kimura ◽  
Shin-ichi Kasai ◽  
Masaaki Inuzuka ◽  
Osami Yasukura
Keyword(s):  
Vector Spaces ◽  
Type I ◽  
Prehomogeneous Vector Spaces

scholarly journals Order 3 Elements in G2 and Idempotents in Symmetric Composition Algebras

2018 ◽  
Vol 70 (5) ◽  
pp. 1038-1075 ◽  
Author(s):  
Alberto Elduque
Keyword(s):  
Conjugacy Classes ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Exceptional Groups ◽  
Composition Algebras ◽  
Characteristic 3

AbstractOrder three elements in the exceptional groups of type G2 are classiûed up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is obtained. Idempotents have played a key role in the study and classification of these algebras.Over an algebraically closed field, there are two conjugacy classes of order three elements in G2 in characteristic not 3 and four of them in characteristic 3. The centralizers in characteristic 3 fail to be smooth for one of these classes.

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