scholarly journals RESTRICTED CARTAN TYPE LIE ALGEBRAS AND THE COADJOINT REPRESENTATION

2015 ◽  
Vol 20 (2) ◽  
pp. 495-505
Author(s):  
MARTIN MYGIND
Keyword(s):  
Lie Algebras ◽  
Coadjoint Representation ◽  
Cartan Type

Restricted Envelopes of Lie Superalgebras

2015 ◽  
Vol 22 (02) ◽  
pp. 309-320
Author(s):  
Liping Sun ◽  
Wende Liu ◽  
Xiaocheng Gao ◽  
Boying Wu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Cartan Type ◽  
Modular Lie Algebras ◽  
Modular Lie Superalgebras

Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.

From Diffeomorphisms to Dark Energy?

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2467-2474 ◽  
Author(s):  
Vincent G. J. Rodgers ◽  
Takeshi Yasuda
Keyword(s):  
Dark Energy ◽  
Lie Algebras ◽  
Virasoro Algebra ◽  
Two Dimensions ◽  
Coadjoint Orbits ◽  
Coadjoint Representation ◽  
Natural Setting ◽  
Affine Lie Algebras ◽  
Yang Mills ◽  
Geometric Action

There are two physical actions that have a natural setting in terms of the coadjoint representation of the algebra of diffeomorphisms and of affine Lie algebras. One is the usual geometric action that comes from coadjoint orbits. The other action lives on the phase space that is transverse to the orbits and are called transverse actions, where Yang-Mills theory in two dimensions is an example. Here we show that the transverse action associated with the Virasoro algebra might contain clues for a theory for dark energy. These actions might also suggests a mechanism for symmetry changing.

Classification of forms of restricted simple lie algebras of cartan type

1991 ◽  
Vol 19 (6) ◽  
pp. 1603-1628 ◽  
Author(s):  
Shirlei Serconek ◽  
Robert Lee Wilson
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Cartan Type
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