Let o be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite o-module M of rank two. The main emphasis is on the interaction between the different groups and their representations. An induction scheme is developed in order to study the whole family of these groups coherently. The results ob...

We study conditions on a C∗-dynamical system (A,G,α) under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of G on the primitive ideal space Prim(A) give primitive ideals (resp. irreducible representations) of the crossed product A⋊α G. The results build on earlier results of Sauvageot [17] and others, and will correct a (possibly overly o...

We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of genera...

In this paper, we introduce a modified Van der Waerden algorithm to decompose a variety into the union of irreducible varieties. We give an effective representation for irreducible varieties obtained by the algorithm, which allows us to obtain an irredundant decomposition easily. We show that in the zero dimensional case, the polynomial systems for the irreducible varieties obtained in the Van ...

For a radical monomial ideal I in a normal semigroup ring k[Q], there is a unique minimal irreducible resolution 0 → k[Q]/I → W 0 → W 1 → · · · by modules W i of the form ⊕ j k[Fij ], where the Fij are (not necessarily distinct) faces of Q. That is, W i is a direct sum of quotients of k[Q] by prime ideals. This paper characterizes Cohen–Macaulay quotients k[Q]/I as those whose minimal irreducib...

We give the definition of D-invariant points on an irreducible algebraic hypersurface V in RN. show that every regular point quadratic RN is D-invariant. prove local Taylor interpolation projector at a 2 ideal if and only

In this paper we use the concept of wavelet sets as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary n×n integer dilation matrix as a direct integral of irreducible monomial representations. In so doing we generalize a result of F. Martin and A. Valette in which they show that the wavelet representation is weakly equiva...

Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the distance d(P) ≤ 2genus(Q). More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either • P and Q can be well-separated or • P and Q are isotopic or

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface (T, `) corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to express wall-crossings as Mukai flops and show that the moduli spaces are projective.

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal. 1 2