We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism tangent bundle. Such are examples non-Riemannian holonomy reduction, and (in complexified setting) appear in Bridgeland stability conditions moduli spaces Calabi-Yau three-folds. Using twistor methods we show that, dimension four - where there is connection wi...

where K is a subfield of even index at most 10 in a primitive cyclotomic field Q(ζp), or a subfield of index 2 in Q(ζpq) or Q(ζpα ). This result generalizes previous work of Brumer, Mestre, and Tautz-Top-Verberkmoes. Our curves are constructed as branched covers of the projective line, and the endomorphisms arise as quotients of double coset algebras of the Galois groups of these coverings. In ...

We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element.

We show that if A is a stable basis algebra satisfying the distributivity condition, then B is a reduct of an independence algebra A having the same rank. If this rank is finite, then the endomorphism monoid of B is a left order in the endomorphism monoid of A.

In a joint paper with Jan Schröer we have shown that a module M over a special biserial algebra A with ExtA(M, M) = 0 has gentle stable endomorphism algebra. In the present note we interpret this result and study the gentle algebras which occur as stable endomorphism algebras of modules over the alternating group of degree 4 in characteristic 2.

In this paper we characterize pairs of Rosenberg relations (ρ, σ) with the property that the endomorphism monoid of one of the relations is properly contained in the endomorphism monoid of the other relation. We focus on the situations where one of the relations is a partial order, or a central relation. AMS Mathematics Subject Classification (2000): 08A35, 06A06

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