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Paper IPM / M / 16848  


Abstract:  
Following the definition of a root basis of an affine root system, we define a base of the root system R of an affine Lie superalgebra to be a linearly independent subset B of the linear span of R such that B\sub R and each root can be written as a linear combination of elements of B with integral coefficients such that all coefficients are nonnegative or all coefficients are nonpositive.
Characterization and classification of bases of root systems of affine Lie algebras are known in the literature; in fact, up to ±1multiple, each base of an affine root system is conjugate with the standard base under the Weyl group action.
In the super case, the existence of those selforthogonal roots which are not orthogonal to at least one other root, makes the situation more complicated. In this work, we give a complete characterization of bases of the root systems of twisted affine Lie superalgerbas. We precisely describe and classify them.
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