Piecewise Hereditary One-Point Extensions

One-point extensions of locally compact paracompact spaces

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

Skew group algebras of piecewise hereditary algebras are piecewise hereditary

The aim of this paper is twofold. First, we show that the main results of HappelRickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose c...

Simple One - Point Extensions of Tournaments

x->y,x=y,y->x holds. Here x -+ y expresses the fact that {x, y} e -+ and we sometimes write this in the alternative form y <--x . Extending the notation to subsets of T we write A --+ B or B is a subtournament of .l, and i is an extension of ,T', if T' e T and -+' is the restriction of --+ to T' ; we will usually writ...

One-point extensions of finite inversive planes

A one-point extension of an egglike inversive plane of order n exists if, and only if, n is 2 or 3. Hence there are no 4-(18,6,1) designs and no 4-(66,10,1) designs. An inversive plane of order n is a one-point extension of an affine plane of ordern, that is, a 3-(n + 1,n + 1,1) design. An ovoid of PG(3, q), q > 2, is a set of q2 + 1 points, no three collinear. An ovoid of PG(3, 2) is a set of ...

Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type