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Every tripotent e of a generalized Jordan triple system J of order l uniquely defines a decomposition into the direct sum of l2+2l components. This decomposition generalizes the known Peirce decomposition of a Jordan triple system and of a generalized Jordan triple system of second order, and is the first step in determining the structure of a generalized Jordan triple system in terms of the tripotent.
The commutative algebra of invariants of a Lie super-algebra need not be affine, but does have a common ideal with an affine algebra, in all the known examples. This leads us to extend a class of algebras C to a class which we call ''nearly C'', by admitting those algebras C having a common ideal A with an algebra (containing C) in C such that C/A C. We generalize this notion slightly, study the...
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