Homogeneous algebras via homogeneous triples

2021 ◽  
Vol 566 ◽  
pp. 259-282
Author(s):  
E. Marcos ◽  
Y. Volkov
Keyword(s):  
1980 ◽  
Vol 11 (1) ◽  
pp. 149-158 ◽  
Author(s):  
B. Csákány
Keyword(s):  

2002 ◽  
Vol 72 (1) ◽  
pp. 47-56 ◽  
Author(s):  
L. G. Sweet ◽  
J. A. Macdougall

AbstractAn algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let La denote left multiplication by any nonzero element a ∈ A. Several results are proved concerning the structure of A in terms of La. In particular, it is shown that A decomposes as the direct sum A = ker La Im La. These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.


2001 ◽  
Vol 76 (2) ◽  
pp. 100-108 ◽  
Author(s):  
J. Herzog ◽  
G. Restuccia
Keyword(s):  

2003 ◽  
Vol 261 (1) ◽  
pp. 172-185 ◽  
Author(s):  
Roland Berger ◽  
Michel Dubois-Violette ◽  
Marc Wambst
Keyword(s):  

1971 ◽  
Vol 1 (1) ◽  
pp. 254-260 ◽  
Author(s):  
D. B. Smith
Keyword(s):  

1972 ◽  
Vol 22 (3) ◽  
pp. 1-19 ◽  
Author(s):  
Colin Bennett ◽  
John E. Gilbert

1975 ◽  
Vol 59 (2) ◽  
pp. 585-594 ◽  
Author(s):  
Lowell Sweet
Keyword(s):  

1973 ◽  
Vol 79 (3) ◽  
pp. 217-220 ◽  
Author(s):  
B. Ganter ◽  
Jerzy Płonka ◽  
H. Werner
Keyword(s):  

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