Optimal $SL(2)$-homomorphisms

Lattice Homomorphisms Induced by Group Homomorphisms

Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

POMDP Homomorphisms

The problem of finding hidden state in a POMDP and the problem of finding abstractions for MDPs are closely related. In this paper, we analyze the connection between existing Predictive State Representation methods [3] and homomorphic reductions of Markov Processes [5, 6]. We formally define a POMDP homomorphism, then extend PSR reduction methods to find POMDP homomorphisms when the original PO...

n-Homomorphisms

On SL2(Z) and Topology

FP (g) = trgKerP − trgCokerP ∈ R(S) where R(S1) is the character ring of the S1-modules. We say that P is rigid with respect to this S1-action, if FP (g) is independent of g. Two well-known examples of rigid elliptic operators are the signature operator ds and the Dirac operator D [AH]. Now let L̃Spin(2l) denote the central extension of the loop group LSpin(2l) and E be a positive energy represe...

DERIVED EQUIVALENCE IN SL2(p)

We present a proof that Broué’s Abelian Defect Group Conjecture is true for the principal p-block of the group SL2(p). Okuyama has independently obtained the same result using a different approach.