Abstract In this paper, we study the groups of isometries and set bi‐Lipschitz automorphisms spectral triples from a metric viewpoint, in propinquity framework Latrémolière. particular, prove that these sets are compact automorphism group triple ‐algebra with respect to Monge–Kantorovich metric, which induces topology pointwise convergence. We then necessary sufficient condition for convergence...

In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon–Nikod´ym property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the β-compactness, the β-...

The (real) GraviGUT algebra is an extension of the spin(11, 3) algebra by a 64dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra into the quaternionic real form of E8. We clarify the definition, showing that there is only one possibility, and then prove that the GraviGUT algebra cannot be e...

This work is an investigation into the structure and properties of supersymmetric hypermatrix Lie algebra generated by elements of the dihedral group D3. It is based on previous work on the subject of supersymmetric Lie algebra (Schreiber, 2012). In preview work I used several new algebraic tools; namely cubic hypermatrices (including special arrangements of such hypermatrices) and I obtained a...

A superspace formulation for the Batalin Vilkovisky formalism (also called fieldantifield quantization ) with extended BRST invariance (BRST and anti-BRST invariance ) for gauge theories with closed algebra is presented. In contrast to a recent formulation, where only BRST invariance holds off shell, two collective sets of fields are introduced and an off shell realization of the extended algeb...

As a fundamental notion, the free differential algebra on set is concretely constructed as polynomial variables. Such construction not known for more general notion of an algebra, from left adjoint functor forgetful algebras to algebras, instead sets. In this paper we show that generator-relation properties base can be extended algebra. More precisely, Gr\"obner-Shirshov basis property allowing...

In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a C∞-algebra and does not generalize to a...