Let Λ be a finite-dimensional associative algebra. The torsion classes of mod Λ form a lattice under containment, denoted by tors Λ. In this paper, we characterize the cover relations in tors Λ by certain indecomposable modules. We consider three applications: First, we show that the completely join-irreducible torsion classes (torsion classes which cover precisely one element) are in bijection...

The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the infrared stable fixed point of the effective scalar theory. ⋆ On leave from Pedagogical Institute, 634041 Tomsk, Russia In a recent paper [1] the trace anomaly induced dynamics of...

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level. 1 E-mail: [email protected] Supported in part by RFFR grant # 94-02 03665-a and ISF grant # RFL300 E-mail: [email protected]

Torsion appears in a natural way in modern formulations of the gravitational theories. In this work we study several aspects of the interplay between the Standard Model and a classical gravitational background with torsion. In particular we consider the problem of the gauge and gravitational anomalies, B and L anomalies, the effective action for the torsion and the propagation of electromagneti...

The first author’s recent unexpected discovery of torsion in the integral cohomology of the Tübingen Triangle Tiling has led to a reevaluation of current descriptions of and calculational methods for the topological invariants associated with aperiodic tilings. The existence of torsion calls into question the previously assumed equivalence of cohomological and K-theoretic invariants as well as ...

Abstract We generalize Einstein’s General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed the Cambridge group. GTG a “spin-torsion” theory, according which, gravitational effects are described pair of gauge fields defined over flat Minkowski background spacetime. The con...

For both f(R) theories of gravity with an independent symmetric connection (no torsion), usually referred to as Palatini f(R) gravity theories, and for f(R) theories of gravity with torsion but no non-metricity, called U4 theories, it has been shown that the independent connection can actually be eliminated algebraically, as long as this connection does not couple to matter. Remarkably, the out...

First, we show that a compact object C in a triangulated category, which satisfies suitable conditions, induces a t-structure. Second, in an abelian category we show that a complex P of small projective objects of term length two, which satisfies suitable conditions, induces a torsion theory. In the case of module categories, using a torsion theory, we give equivalent conditions for P to be a t...

We generalize to higher algebraic $K$-theory an identity (originally due Milnor) that relates the Reidemeister torsion of infinite cyclic cover its Lefschetz zeta function. Our involves a invariant, endomorphism torsion, parametrized family endomorphisms as well function such family. also exhibit several examples families having non-trivial torsion.