On the Lie algebra associated to S-unitary matrices

Real dimension of the Lie algebra of S-skew-Hermitian matrices

“…In contrast, our motivation is to provide an insight on the structure of u S and find a convenient Lie algebra basis. This paper continues the authors' earlier works ( [3] and [4, Corollary 2.1]) on u S where S is normal and nonsingular. In particular, we generalize the dimension formula given in [3,Theorem 3.19] by eliminating the normality condition on S.…”

“…This paper continues the authors' earlier works ( [3] and [4, Corollary 2.1]) on u S where S is normal and nonsingular. In particular, we generalize the dimension formula given in [3,Theorem 3.19] by eliminating the normality condition on S.…”

“…In [3], the problem of determining whether two Lie groups U S and U T are isomorphic is investigated. The strategy employed in the paper is to look at the associated Lie algebras u S .…”

“…Note that S is not normal and as such, [3,Theorem 3.19] cannot be used. The cosquare of S is similar to J 1 (1) ⊕ J 2 (1).…”