We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any “Theory of Everything” obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representationtheoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras along the lines of ...

People are typically poor at telling apart truthful and deceptive statements. Based on the Unconscious Thought Theory, it has been suggested that poor lie detection arises from the intrinsic limitations of conscious thinking and can be improved by facilitating the contribution of unconscious thought (UT). In support of this hypothesis, Reinhard et al. (2013) observed improved lie detection amon...

A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of these algebras is given explicitly.

We derive a new formula for the supersymmetric Schur polynomial sλ(x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m/n). In particular, we show how a character formula due to Kac and Wakimoto can be applied to covariant representations, leading to a new expression for sλ(x/y). This new expression gives rise to a determinantal formula for sλ(x/y). I...

Let g be a semisimple complex Lie algebra and θ ∈ Aut g be an involution. If g = k⊕ p is the decomposition associated to θ , define a Lie subalgebra of End p by k̃ = {X : ∀f ∈ S(p∗)k, X.f = 0} . We prove that adp(k) = k̃ if, and only if, each irreducible factor of rank one of the symmetric pair (g, k) is isomorphic to (so(q + 1), so(q)) .

In this paper we take a close look at Lie derivatives on a Finsler bundle and give a geometric meaning to the vanishing of the mixed curvature of certain covariant derivatives on a Finsler bundle. As an application, we obtain some characterizations of Landsberg manifolds.

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. For finite-dimensional ones we show that if they are semisimple as associative algebras then they are standard, on the other hand, if they are semisimple as Lie algebras then their associative products are trivial. We also give the descriptions of ...

Asymptotic normalization coefficients (ANC) determine the overall of cross sections peripheral radiative capture reactions. In present paper, we treat ANC $C$ for virtual decay $^{16}$O$(0^+; 6.05$ MeV)$\to \alpha+^{12}$C(g.s.), known values which are characterized by a large spread $(0.29-1.65)\times 10^3$ fm$^{-1/2}$. The is found analytic continuation in energy $\alpha^{12}$C $s$-wave scatte...

Recent evidence suggests that high-redshift Ly-alpha emitting galaxies (LAEs) with logL(Ly-alpha) > 43.5 erg/s, referred to as ultraluminous LAEs (ULLAEs), may show less evolution than lower-luminosity in the redshift range z=5.7-6.6. Here we explore of velocity widths emission lines over this interval. We use new wide-field, narrowband observations from Subaru/Hyper Suprime-Cam provide a sampl...

Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holon-omy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for t...