It is stated in the exterior algebra Wiki entry that the Hodge dual becomes an antipode map, with which the exterior bialgebra becomes a Hopf algebra.
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The exterior algebra is also named "'Grassmann algebra "'after Hermann Grassmann, who introduced it as " extended " algebras.
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Especially for supporting PsiEpsilon in 2012 for incorrect edits to exterior algebra . " ?lk " 07 : 19, 27 October 2013 ( UTC)
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If the quadratic form is fully degenerate, the inner product of any two vectors is always zero, and the geometric algebra is then simply an exterior algebra.
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In view of structure theorems on Hopf algebras by tensor product of a polynomial ring on generators of even degree with an exterior algebra on generators of odd degree.
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This can be achieved by replacing the cross product by the exterior product in the language of exterior algebra, and angular momentum becomes a contravariant second order antisymmetric tensor
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A finite dimensional exterior algebra may be equipped with a coproduct and a counit ( described in the exterior algebra Wiki entry ), with which it becomes a bialgebra.
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A finite dimensional exterior algebra may be equipped with a coproduct and a counit ( described in the exterior algebra Wiki entry ), with which it becomes a bialgebra.
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Furthermore, Rothe worked outside his teaching activity on mathematical problems like Hermann Grassmann's " Ausdehnungslehre " ( theory of extension, or exterior algebra ).
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The construction of the bialgebra here parallels the construction in the tensor algebra article almost exactly, except for the need to correctly track the alternating signs for the exterior algebra.
