We define an index for 2D G-invariant invertible states of bosonic lattice systems in the thermodynamic limit a finite symmetry group G with unitary action. show that this is invariant protected phase.

On the topology of the group of invertible elements – A Survey – The topological structure of the group of invertible elements in a unital Banach algebra (regular group for short) has attracted topologists from the very beginning of homotopy theory. Be it for its own sake simply to show the instrumental power of newly invented methods or because there were important applications, the most notab...

We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We then give a combinatorial classification of reductive monoids by means of the theory of spherical varieties.

We consider the semigroup Ext(A, B) of extensions of a separable C *-algebra A by a stable C *-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext −1/2 (A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext 1/2 (A, B) is homotopy invariant and that it coincides with the functor of homoto...

in this paper, we introduce fuzzy banach algebra and study the properties of invertible elements and its relation with opensets. we obtain some interesting results.

We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...