THE CLASSIFICATION OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS

• We say that an indecomposable Cartan matrix A with entries in the ground field is almost affine if the Lie (super) algebra determined by it is not finite dimensional or affine (Kac-Moody) but the Lie sub(super) algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting on the main diagonal, is the sum of finite dimensional or affine Lie (super) algebras. A Lie (super) algebra with Cartan matrix is said to be almost affine if it is not finite dimensional or affine (Kac-Moody), and all of its Cartan matrices are almost affine. We list all almost affine Lie superalgebras over complex numbers with indecomposable Cartan matrix correcting two earlier claims of classification.

Subject headings

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

Keyword

Hyperbolic Lie superalgebra

almost affine Lie superalgebra

Mathematical physics

Matematisk fysik

Mathematics

matematik

Publication and Content Type

ref (subject category)

art (subject category)