JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 2, Pages 311 - 322
(August 2004)
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ON SEPARABLE SUBALGEBRAS OF A HOPF GALOIS AZUMAYA EXTENSION
George Szeto (U. S. A.) and Lianyong Xue (U. S. A.)
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Abstract: Let B be an
H*-Galois
Azumaya extension where H*
is the dual Hopf algebra of a finite
dimensional Hopf algebra H over a field k.
It is shown that any separable subalgebra A of
BH
is
the H-invariant subalgebra of a unique H*-Galois
Azumaya extension D in B such that
D commutes with VBH(A)
the commutator subalgebra of A in BH.
Consequently, some correspondences between
several classes of separable subalgebras of B
are obtained. |
Keywords and phrases: separable extensions,
Azumaya algebras, Galois extensions, Galois Azumaya
extensions, H*-Galois
extensions, H*-Galois
Azumaya extensions. |
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