Topological invariants of three-manifolds from U_q(osp(1|2n))

Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds

The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra U_q(osp(1|2n)) over C is considered with q a primitive N^th root of unity for all integers N >= 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U_q^(N)(osp(1|2n)) = U_q(osp(1|…

非半单拓扑场论及从 osp(1|2) 来的 $\widehat{Z}$-不变量

Non-semisimple topological field theory and $\widehat{Z}$-invariants from $\mathfrak{osp}(1 \vert 2)$

本文基于 Lie 超代数 osp(1|2) 构造非半单拓扑场论，并建立了与物理中 Z-不变量的关联。

Towards a q-series for osp(2|2n)

A series invariant for a certain class of closed 3-manifolds associated with a type I Lie superalgebra sl(m|n) was introduced recently. We find a q-series for the other Lie superalgebra of the same type of the minimum rank.

Lickorish Invariant And Quantum OSP(1|2)

Lickorish's method for constructing topological invariants of 3 - manifolds is generalized to the quantum supergroup setting. An invariant is obtained by applying this method to the Kauffman polynomial arising from the vector representation of Uq(osp(1|2)). A transparent proof is also given showing that this invariant is equivalent to the Uq(osp(1|2)) invariant obtained in an earlier publication.

$SO(3)$与$OSp(1|2)$群的$\u017d$不变量

$\hat Z$- invariant for $SO(3)$ and $OSp(1|2)$ Groups

本文聚焦$SO(3)$群与正交辛超群$OSp(1|2)$的$\u017d$不变量，借助联系$SU(2)$与这两类群纽结不变量的变量替换，推导其作为整数系数$q$级数的显式形式。

A Hennings type invariant of $3$-manifolds from a topological Hopf superalgebra

We prove the unrolled superalgebra $\mathcal{U}_ξ^{H}\mathfrak{sl}(2|1)$ has a completion which is a ribbon superalgebra in a topological sense where $ξ$ is a root of unity of odd order. Using this ribbon superalgebra we construct its universal invariant of links. We use it to construct an invariant of $3$-manifolds of Hennings type.