Let A be a finite dimensional hereditary algebra over an algebraically closed field and A(m) the m-replicated algebra of A. We prove that the representation dimension of A(m) is at most three, and that the dominant dimension of A(m) is at least m.

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

Let G be a connected semisimple Lie group with no compact factors and finite center and let T be a lattice in G (i.e. a discrete subgroup such that G/T has a finite invariant measure). Let n be a representation of G on some vector space V. Borel [Bo] proved that if n is a rational representation and V is finite dimensional then every T-invariant line in V is G-invariant; in fact, this is equiva...

A Riemann–Roch theorem is a theorem which asserts that some algebraically defined wrong–way map in K –theory agrees or is compatible with a topologically defined one [BFM]. Bismut and Lott [BiLo] proved a Riemann–Roch theorem for smooth fiber bundles in which the topologically defined wrong–way map is the homotopy transfer of Becker–Gottlieb and Dold. We generalize and refine their theorem. In ...

Given a quaternionic form $$\textrm{G}$$ of p-adic classical group (p odd) we classify all cuspidal irreducible representations with coefficients in an algebraically closed field characteristic different from p. We prove two theorems: At first: Every representation is induced type, i.e. certain compact open subgroup , constructed $$\beta $$ -extension and finite group. Secondly show that intert...