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It is shown that two affine Kac–Moody groups are isomorphic to each other if and only if their root systems, as well as the base fields, are isomorphic to each other. The analogous property for the related loop groups is also found to be true.
Let A be a commutative domain. We prove that both implications A atomic ⇒ A((X)) atomic , and A((X)) atomic ⇒ A atomic fail in general.
The purpose of this paper is to use geometric modules and path matrix morphisms of construct a continuously controlled K-theory with variable coefficients. The theory constructed here can be thought of as a “pushout” of the boundedly controlled K-theory with variable coefficients constructed...
The X-confluence of a quadratic algebra A defined by generators and relations can be interpreted as an equality between two idempotent endomorphisms acting on tensors of degree three (X is the ordered set of generators). Those endomorphisms are simply defined from the X-reduction operator of A...
In this note we will study the formal completion of the Jacobian of a certain class of curves over p -adic rings. These curves generalize the Legendre family of elliptic curves. As an immediate application, we will describe the representation which is crucial for calculating the initial term of...
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