Quadratic Forms in Infinite Dimensional Vector Spaces

1979 ◽  
Author(s):  
Herbert Gross
Keyword(s):  
Quadratic Forms ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Infinite Dimensional

scholarly journals GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

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