• The center of a commutative ring is itself. • The center of a
skew-field is a
field. • The center of the (full)
matrix ring with entries in a commutative ring consists of -scalar multiples of the
identity matrix. • Let be a
field extension of a field , and an algebra over . Then \operatorname{Z}(R \otimes_k F) = \operatorname{Z}(R) \otimes_k F. • The center of the
universal enveloping algebra of a
Lie algebra plays an important role in the
representation theory of Lie algebras. For example, a
Casimir element is an element of such a center that is used to analyze
Lie algebra representations. See also:
Harish-Chandra isomorphism. • The center of a
simple algebra is a field. == See also ==