Publication: Concept of the fundamental weight and the using in root systems and representations of classical Lie algebras
Abstract
Literatürde klasik cebirler olarak da bilinen $A_N$, $B_N$, $C_N$ ve $D_N$ Lie cebirlerinin kök sistemleri öklid uzayında ortonormal bir baz teşkil eden $\{\epsilon_i\}$ elemanları tarafından tanımlanmaktadır. Bu çalışmada, söz konusu cebirlerin temsil ve kök sistemleri, genelde ortonormal olmayan ve temel ağırlık olarak isimlendirdiğimiz $\{\mu_i\}$ baz elemanları cinsinden yeniden yapılandırılmıştır.
Root systems of $A_N$, $B_N$, $C_N$ and $D_N$ which are also known as classical algebras in the literature, are defined by the elements of $\{\epsilon_i\}$ which establish an orthonormal basis in the euclidean space. In this study, root systems and representations of algebras which mentioned above, are constructed in term of $\{\mu_i\}$ basis elements which are usually non-orthonormal and we define as fundamental weight.
Root systems of $A_N$, $B_N$, $C_N$ and $D_N$ which are also known as classical algebras in the literature, are defined by the elements of $\{\epsilon_i\}$ which establish an orthonormal basis in the euclidean space. In this study, root systems and representations of algebras which mentioned above, are constructed in term of $\{\mu_i\}$ basis elements which are usually non-orthonormal and we define as fundamental weight.