arXiv subjects
Publications and source records attributed to Fred Greensite.
We present a non-physical interpretation of the Cosmological Constant based on a particular algebraic analysis. This also introduces some novel algebraic structures, such as ``unital norms", ``uncurling metrics", and ``partial wedge products".
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally straightforward in general, thereby augmenting the recognized accessible distinguishing features of algebra structure.
As we have previously shown, recognition of an algebra's group of uncurling metrics leads to a generalization of the usual algebra norm and a novel set of isomorphism invariants. It is herein detailed how this arose in the analysis of an unusual Inverse Problems regularization method.
A parametrized family of pseudo-Finsler norms is derived from application of a particular transform procedure to the space of ``normalized" trace forms of any given real finite-dimensional unital associative algebra. The implied parametrized family of dual norms on a connected conic subbundle of the relevant cotangent space supports wavefront phenomena that lead to a trove of novel algebra isomorphism invariants associated with a cascade of caustics typically arising from algebras that do not admit a direct sum decomposition whose non-simple blocks all have dimension less than four. The algebra's commutator subspace can be accessed by reapplying the above procedure at all relevant orders of the algebra's infinitesimal neighborhoods. The general character of this set of invariants appropriately reflects the wildness of the algebra isomorphism problem.
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.