Basis of identities of a three-dimensional simple lie algebra over an infinite field

1989 ◽  
Vol 28 (5) ◽  
pp. 355-368 ◽  
Author(s):  
S. Yu. Vasilovskii
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Infinite Field ◽  
Basis Of Identities ◽  
Simple Lie Algebra

ALGEBRAIC DEFINITION OF TOPOLOGICAL W GRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5193-5211
Author(s):  
SHINOBU HOSONO
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Simple Lie Algebra ◽  
Topological Gravity ◽  
Definition Of ◽  
Extended Theories

We propose a definition of the topological W gravity using some properties of the principal three-dimensional subalgebra of a simple Lie algebra due to Kostant. In our definition, structures of the two-dimensional topological gravity are naturally embedded in the extended theories. In accordance with the definition, we will present some explicit calculations for the W3 gravity.

AUTOMORPHISMS OF CERTAIN NILPOTENT LIE ALGEBRAS OVER COMMUTATIVE RINGS

2007 ◽  
Vol 17 (03) ◽  
pp. 527-555 ◽  
Author(s):  
YOU'AN CAO ◽  
DEZHI JIANG ◽  
JUNYING WANG
Keyword(s):  
Automorphism Group ◽  
Commutative Ring ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Commutative Rings ◽  
Nilpotent Lie Algebras ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Positive Roots ◽  
Nilpotent Subalgebra

Let L be a finite-dimensional complex simple Lie algebra, Lℤ be the ℤ-span of a Chevalley basis of L and LR = R⊗ℤLℤ be a Chevalley algebra of type L over a commutative ring R. Let [Formula: see text] be the nilpotent subalgebra of LR spanned by the root vectors associated with positive roots. The aim of this paper is to determine the automorphism group of [Formula: see text].

scholarly journals THE UNIVERSAL LINK POLYNOMIAL

1992 ◽  
Vol 07 (05) ◽  
pp. 877-945 ◽  
Author(s):  
E. GUADAGNINI
Keyword(s):  
Field Theory ◽  
Closed Form ◽  
Lie Algebra ◽  
Wilson Line ◽  
Expectation Values ◽  
Simple Lie Algebra ◽  
Chern Simons

The solution of the non-Abelian SU (N) quantum Chern–Simons field theory defined in R3 is presented. It is shown how to compute the expectation values of the Wilson line operators, associated with oriented framed links, in closed form. The main properties of the universal link polynomial, defined by these expectation values, are derived in the case of a generic real simple Lie algebra. The resulting polynomials for some simple examples of links are reported.

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