The basic construction
نویسنده
چکیده
In this section we shall assume that all algebras are finite dimensional algebras over an algebraically closed field F. The fact that F is algebraically closed is only for convenience, to avoid the division rings that could arise in the decomposition of Ā just before (4.8) below. Let A ⊆ B be an inclusion of algebras. Then B⊗F B is an (A,A)-bimodule where A acts on the left by left multiplication and on the right by right multiplication. Fix an (A,A)-bimodule homomorphism ε : B ⊗F B −→ A. (1.1) The basic construction is the algebra B ⊗A B with product given by (b1 ⊗ b2)(b3 ⊗ b4) = b1 ⊗ ε(b2 ⊗ b3)b4, for b1, b2, b3, b4 ∈ B. (1.2)
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