One of the easiest examples I can think of for frobenius algebras is a plain ol' matrix algebra with tr : V → k as the co-unit (or equivalently, tr(a⋅b) as the frobenius form). This is enough data to generate a co-multiply comultiplication δ : V → V ⊗ V. This turns out to be μ†, for multiplication μ. Is there any intuition for what this map does (aside from the obvious "do multiplication on the dual space")?
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What is the co-multiply comultiplication of a matrix frobenius algebra? |
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What is the co-multiply of a matrix frobenius algebra?One of the easiest examples I can think of for frobenius algebras is a plain ol' matrix algebra with tr : V → k as the co-unit (or equivalently, tr(a⋅b) as the frobenius form). This is enough data to generate a co-multiply δ : V → V ⊗ V. This turns out to be μ†, for multiplication μ. Is there any intuition for what this map does (aside from the obvious "do multiplication on the dual space")?
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