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Paper   IPM / M / 16848
School of Mathematics
  Title:   Classification of bases of twisted affine root supersystems
  Author(s):  Malihe Yousofzadeh
  Status:   To Appear
  Journal: J. Algebraic Combin.
  Supported by:  IPM
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 non-negative or all coefficients are non-positive. Characterization and classification of bases of root systems of affine Lie algebras are known in the literature; in fact, up to ±1-multiple, 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 self-orthogonal 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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