Advanced Materials Science Research

Super-algebras-Journals

  Graded Lie algebras in the context of supergauge symmetries relating particles from different statistics have recently become a topic of interest in physics. The definition of a superalgebra can be generalized to include cases where the scalar domain is an arbitrary commutative superalgebra associative. Lie superalgebra G there is an associative universal enveloping superalgebra, and the straightforward generalization of the Birkhoff–Witt theorem holds.  Lie superalgebras are initially introduced as Lie algebras of some generalized groups now called formal Lie supergroup. There is no need to say the importance of the representation theory of any algebraic structures when their physical and mathematical applications are concerned. We presented a vector field representation of the color superalgebra bf which is a straightforward extension of the Lie theory to the Z2 ⊗ Z2 setting. However, if we consider a naive extension of Verma modules to the case of bf, we encounter some difficulties. Over algebraically closed positively characteristic fields, we establish when there is a NIS in the deformation (i.e., the result of deformation) of the known finite-dimensional simple Lie (super) algebra. Cartan matrix of any growth with non-symmetrizable Cartan matrix of polynomial growth Lie (super)algebras of vector fields with stringy polynomial coefficients a.k.a. super-conform superalgebras that verifications of simple, restricted Lie algebras. 

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