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We present the formulas for twist quantization of g2, corresponding to the solution of a classical YB equation with support in the eight-dimensional Borel subalgebra of g2. The considered chain of twists consists of the four factors describing the four steps of quantization: Jordanian twist, the two twist factors extending Jordanian twist and the deformed Jordanian or in a second variant additional Abelian twist. The first two steps describe as well the sl(3) quantization. The coproducts are calculated for each step in explicit form, and for that purpose we present new formulas for the calculation of similarity transformations on the tensor product. We introduce new basic generators in universal enveloping algebra U(g2) that provide nonlinearities in the algebraic sector maximally simplifying the deformed coproducts. [ABSTRACT FROM AUTHOR]

We present the formulas for twist quantization of g2, corresponding to the solution of a classical YB equation with support in the eight-dimensional Borel subalgebra of g2. The considered chain of twists consists of the four factors describing the four steps of quantization: Jordanian twist, the two twist factors extending Jordanian twist and the deformed Jordanian or in a second variant additional Abelian twist. The first two steps describe as well the sl(3) quantization. The coproducts are calculated for each step in explicit form, and for that purpose we present new formulas for the calculation of similarity transformations on the tensor product. We introduce new basic generators in universal enveloping algebra U(g2) that provide nonlinearities in the algebraic sector maximally simplifying the deformed coproducts. [ABSTRACT FROM AUTHOR]

Generalized Lie algebras and superalgebras with generators and structure constants taking values in a Grassmann algebra are introduced. Such algebraic structures describe the equal time algebras in the superfield formalism. As an example, the equal time commutators and anticommutators among bilinears made out of the D = 1 quantum superfields describing the supersymmetric harmonic oscillator are considered. [ABSTRACT FROM AUTHOR]