Related papers: Simple derivation of general Fierz-type identities

We use geometric algebra techniques to give a synthetic and computationally efficient approach to Fierz identities in arbitrary dimensions and signatures, thus generalizing previous work. Our approach leads to a formulation which displays…

We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as…

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…

For a single fermionic field, an interpretation of the Fierz identities (which establish relations between the bilinear field observables) is given. They appear closely related to the algebraic class (regular or singular) of the spin 2-form…

Given a central division algebra $D$ of degree $d$ over a field $F$, we associate to any standard polynomial $\phi(z)=z^n+c_{n-1} z^{n-1}+\dots+c_0$ over $D$ a "companion polynomial" $\Phi(z)$ of degree $n d$ with coefficients in $F$ whose…

We study the differential identities of the algebra $M_k(F)$ of $k\times k$ matrices over a field $F$ of characteristic zero when its full Lie algebra of derivations, $L=\mbox{Der}(M_k(F))$, acts on it. We determine a set of 2 generators of…

We prove a universal identity for powers of elements in quadratic algebras, expressing x^m in terms of x and the identity. As a consequence, we obtain a general formula for powers of 2x2 matrices depending only on trace and determinant.…

We prove that the space of cuspidal quaternionic modular forms on the groups of type $F_4$ and $E_n$ have a purely algebraic characterization. This characterization involves Fourier coefficients and Fourier-Jacobi expansions of the cuspidal…

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…

We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…

Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative…

Let $A$ be a $W$-algebra over a field $F$ of characteristic zero, where $W$ is any $F$-algebra. We first develop a comprehensive theory of generalized identities independent of the algebraic structure of $W$, using the multiplier algebra of…

In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…

We define a version of a derived chiral De Rham complex over a locally complete intersection, thereby "chiralizing" a result by Illusie and Bhatt. A similar construction attaches to a graded ring a dg vertex algebra, which we prove to be…

This paper is concerned with the completion of the proof of the Bergman centralizer theorem by using generic matrices based on our previous quantization proof \cite{KBRZh}. Additionally, we establish that the algebra of generic matrices…

Explicit forms are given of matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su(2). We also give a kind of factorization formula of the associated Laguerre polynomials.

Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…

Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as…

Motivated by questions related to the landscape of flux compactifications, we combine new and existing techniques into a systematic, streamlined approach for computing vertical fluxes and chiral matter multiplicities in 4D F-theory models.…

The authors of this article intend to present some results obtained in the study of biderivations of complete Lie algebras. Firstly they present a matricial approach to do this, which was a useful and explanatory tool not only in the study…