Superalgebra

: $A\otimes A ightarrow A$ which is an even morphism of super vector spaces. This means that : $A_iA_j \sube A_{i+j}$ where the subscripts are read modulo 2. As with ordinary Algebras , the multiplication is usually required to be Associative and Unital (although there are important classes of algebras such as Lie Superalgebra s which are neither). The identity element is necessarily even. FURTHER DEFINITIONS The ''even subalgebra'' of a superalgebra ''A'' is the homogeneous subalgebra ''A''₀ spanned by the even elements. It forms an ordinary algebra over ''K''. By contrast, the odd subspace ''A''₁ does not form a subalgebra since the product of any two odd elements is even. A Commutative Superalgebra is one which satisfies a graded version of Commutativity . Specifically, ''A'' is commutative if
	The Set Of All Square	"http://wwwinformationdelightinfo/encyclopedia/entry/supermatrices" class="copylinks">Supermatrices with entries in ''K'' forms a superalgebra denoted by ''M''<sub>''p''''q''</sub>(''K'') This algebra may be identified with the algebra of endomorphisms of a super vector space of dimension ''p''''q''

	CATEGORIES ABOUT SUPERALGEBRA

	super linear algebra

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