ABSTRACT
Para-Fermi statistics and Fermi statistics are known to be associated with particular representations of the Lie algebra https://www.w3.org/1998/Math/MathML"> so ( 2 n + 1 ) ≡ B n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq8395.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . Similarly paraBose and Bose statistics are related with the Lie superalgebra https://www.w3.org/1998/Math/MathML"> osp ( 1 ∣ 2 n ) ≡ B ( 0 ∣ n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq8396.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . We develop an algebraical framework for the generalization of quantum statistics based on the Lie algebras https://www.w3.org/1998/Math/MathML"> A n , B n , C n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq8397.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> D n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq8398.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
