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In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.
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The aim of this paper is to discuss a construction of a class of linear isomorphisms σ:S(g)→U(g) which commute with the adjoint representation.
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However, there are many examples that do not arise from this construction.
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Using the properties ofn-Hopf algebras we show that certain spaces do not admit the structure of ann-valued group and that certain commutativen-valued groups do not arise by applying then-coset construction to any commutative group.
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We give complete proofs of the K-theoretic construction of the quantized enveloping algebra of affine gl(n) sketched in [GV].
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