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It is presented a complete categorical description of one of the main differentiation algorithms for representations of posets with involution — Differentiation II — constructed originally by the second author at the end of the 80's on the base of the matrix approach. A similar categorical description of some simpler additional differentiations is given as well. [ABSTRACT FROM AUTHOR]

The notion of tameness for the derived category of a finite dimensional algebra is introduced and standard properties are established. This is based on classical tameness definitions of Drozd and Crawley-Boevey for the category of finite dimensional representations. [ABSTRACT FROM AUTHOR]

It is well known that there are 16 two-dimensional reflexive polytopes up to lattice isomorphism. One can check directly from the list that the number of lattice points on the boundary of such a polytope plus the number of lattice points on the boundary of the dual polytope is always 12. It turns out that two-dimensional reflexive polytopes correspond to certain relations of two generators A and B of SL[sub 2](Z) of length 12. We generalize this correspondence to reflexive configurations with winding number w and relations of length 12w. [ABSTRACT FROM AUTHOR]