In this paper we consider the ordered by inclusion lattice Part(M) of all partitions of a countable set M. The lattice Part(M) is a semigroup with respect to the operation Λ which maps two partitions to their greatest ...

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain ...

Vitaliy Ivanovych Sushchansky was born on November 11, 1946 in Khodorkiv in Zhytomyr region west of Kyiv. He died half a month before his seventieth birthday on October 29, 2016 in Gliwice, Poland. He was an outstanding ...

We give a classification of representations of the Kleinian 4-group up to weak equivalence.

As observed by Eilenberg and Moore (1965), for a monad F with right adjoint comonad G on any category A, the category of unital F-modules AF is isomorphic to the category of counital G-comodules AG. The monad F is ...

We define representations of weighted posets and construct for them reflection functors. Using this technique we prove that a weighted poset is of finite representation type if and only if its Tits form is weakly positive; ...

Two fields are Witt equivalent if, roughly speaking, they have the same quadratic form theory. Formally, that is to say that their Witt rings of symmetric bilinear forms are isomorphic. This equivalence is well understood ...

We define a wreath product of a Lie algebra L with the one-dimensional Lie algebra L1 over Fp and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of ...