Deligne's topological central extension is universal

Universal Central Extension of Current Superalgebras

Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras  are very impo...

Topological extension of parity automata

The paper presents a concept of a coloring — an extension of deterministic parity automata. A coloring K is a function A∗ → N satisfying ∀α∈Aω lim inf n→∞ K(α n) <∞. Every coloring defines a subset of A by the standard parity condition [K] = { α ∈ A : lim inf n→∞ K(α n) ≡ 0 mod 2 } . We show that sets defined by colorings are exactly all ∆3 sets in the standard product topology on A. Furthermor...

Tower extension of topological constructs

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct C(L), called the tower extension of C (indexed by L). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spac...

Universal symmetry-protected topological invariants for symmetry-protected topological states

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Symmetry-protected topological (SPT) states are short-range entangled states with a symmetry G. They belong to a ne...

The Hopf Extension Theorem for Topological Spaces