Quantized enveloping superalgebra of type P

Webs of Type P

“…In [1] Ahmed-Grantcharov-Guay introduced a quantum superalgebra of type P via FRT formalism. As an outcome of the construction they obtain a Hopf superalgebra with a quantum analogue of the natural representation and an action of the braid group on its iterated tensor products.…”

“…The following relations hold in p-Web m , for all valid 1 ≤ i, j ≤ m, and a ∈ Z m ≥0 . [e (1) [i,i+1] , f…”

Webs of type P

“…by(3.4) and(3.5), so it follows that S ′ m ⊆ S m , completing the proof.∎ If k is a field of characteristic zero, then morphisms in p-Web m are generated under composition by the set {b[1],a | a ∈ Z ≥0 } when m = 1, and by Y 0 (m) ∶= { e(1) …”

“…In [1], Ahmed, Grantcharov, and Guay introduced a quantum superalgebra of type P via the FRT formalism. As an outcome of the construction, they obtain a Hopf superalgebra with a quantum analogue of the natural representation and an action of the braid group on its tensor powers.…”

Howe Duality of Type P

“…is not semisimple and it would be interesting to describe its indecomposable summands. In a different direction, Ahmed, Grantcharov, and Guay defined a quantized enveloping superalgebra of type P using the FRT formalism [1]. As those authors point out, it is an open question to provide a Drinfeld-Jimbotype presentation of this quantized enveloping superalgebra which, presumably, could be chosen to be a quantization of Definition 3.1.1.…”