For the all-ones lower triangular matrices, the upper and lower bounds on rigidity are known to match [13]. In this short note, we apply these techniques to the allones extended lower triangular matrices, to obtain upper and lower bounds with a small gap between the two; we show that the rigidity is θ( 2 r ).

A triangular matrix algebra over a field k is defined by a triplet (R, S, M) where R and S are k-algebras and RMS is an SR-bimodule. We show that if R, S and M are finite dimensional and the global dimensions of R and S are finite, then the triangular matrix algebra corresponding to (R, S, M) is derived equivalent to the one corresponding to (S, R, DM), where DM = Homk(M, k) is the dual of M , ...

In this paper, we present a new lifting algorithm for triangular sets over general p-adic rings. Our contribution is to give, for any p-adic triangular set, a shifted algorithm of which the triangular set is a fixed point. Then we can apply the relaxed recursive p-adic framework and deduce a relaxed lifting algorithm for this triangular set. We compare our algorithm to the existing technique an...

the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.

Some approaches to 2d gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.