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In mathematics and theoretical physics, a superalgebra is a Z 2-graded algebra. [1] That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading. The prefix super-comes from the theory of supersymmetry in theoretical physics.
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
A Poisson algebra is an associative algebra together with a Lie bracket. If the algebra is given a Z 2-grading, such that the Lie bracket becomes a Lie superbracket, then one obtains the Poisson superalgebra. If, in addition, the associative product is made supercommutative, one obtains a supercommutative Poisson superalgebra.
Supermathematics is the branch of mathematical physics which applies the mathematics of Lie superalgebras to the behaviour of bosons and fermions.The driving force in its formation in the 1960s and 1970s was Felix Berezin.