论文标题
量子喷气捆
Quantum Jet Bundles
论文作者
论文摘要
我们在可能的非交通式代数$ a $上制定了一条喷气式捆绑包，配备了免费连接。在三阶射流及以上所需的条件中，连接也是平坦的，其“广义编织张量” $σ：ω^1 \otimes_aΩ^1 \ 1 \ toω^1 \otimes_aΩ^1 $ ofe Yang-Baxter方程或编织关系。我们还涵盖了给定的“向量捆绑包”的案例，其形式超过了$ a $，并带有平坦的双模块连接，其编织$σ_e$遵守了彩色的编织关系。示例包括带有2个循环微积分的置换组$ s_3 $，$ m_2（\ bbb c）$，二维为二维的二十款模型量子时空和$ \ bbb c_q [sl_q [sl_2] $ for $ q $ q $ q $ $ q $ $ a第4个统一根。
We formulate a notion of jet bundles over a possibly noncommutative algebra $A$ equipped with a torsion free connection. Among the conditions needed for 3rd-order jets and above is that the connection also be flat and its `generalised braiding tensor' $σ:Ω^1\otimes_AΩ^1\to Ω^1\otimes_AΩ^1$ obey the Yang-Baxter equation or braid relations. We also cover the case of jet bundles of a given `vector bundle' over $A$ in the form of a bimodule $E$ with a flat bimodule connection with its braiding $σ_E$ obeying the coloured braid relations. Examples include the permutation group $S_3$ with its 2-cycles calculus, $M_2(\Bbb C)$, the bicrossproduct model quantum spacetime in two dimensions and $\Bbb C_q[SL_2]$ for $q$ a 4th root of unity.
