Compositio Mathematica



On Central Elements in the Universal Enveloping Algebras of the Orthogonal Lie Algebras


Minoru Itoh a1 and Tôru Umeda a2
a1 Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan
a2 Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan

Article author query
itoh m   [Google Scholar] 
umeda t   [Google Scholar] 
 

Abstract

We present an analogy of the famous formula that the square of the Pfaffian is equal to the determinant for an alternating matrix for the case where the entries are the generators of the orthogonal Lie algebras. This identity clarifies the relation between the two sets of central elements in the enveloping algebra of the orthogonal Lie algebras. We employ systematically the exterior calculus for the proof.


Key Words: center of universal enveloping algebra; orthogonal Lie algebra.