论文标题
虚拟箭头temberley- lieb代数，马尔可夫痕迹和虚拟链接不变式
Virtual an arrow Temperley--Lieb algebras, Markov traces, and virtual link invariants
论文作者
论文摘要
令r f = z [a $ \ pm $ 1]是变量a中的laurent多项式的代数，让r a = z [a $ \ pm $ 1，z 1，z 1，z 2，。 。 ..。对于n $ \ ge $ 1，我们用vb n n strands上的虚拟辫子组表示。我们定义了代数{Vtl N（r f）} $ \ infty $ n = 1和{atl n（r a）} $ \ infty $ n = 1的两个塔。对于每个N $ \ ge $ 1，我们确定VTL N（R F）和ATL N（R A）的演示文稿。我们确定同构的序列{$ρ$ f n：r f [vb n] $ \ rightarrow $ vtl n（r f）} $ \ infty $ n = 1 and {$ρ$ a n：r a [vb n] $ \ rightarrow $ \ rightarrow $ at $ at n（r a）} $ \ a f in（r a）} $ \ in ftty $ n = 1，我们确定Mark. $ \ rightArrow $ r f} $ \ infty $ n = 1和{t a n：atl n（r a）$ \ rightarrow $ r a} $ \ infty $ n = 1，我们证明，从这些马尔可夫痕迹获得的虚拟链接的不变性链接是第一个Trace和Arrow polynom的F-PolyNomial trace trace and arrow polynomial的f-Polynomial。我们表明，对于每个n $ \ ge $ 1，标准的temperley-lieb代数tl n都嵌入VTL N（R F）和ATL N（r a）中，并且对{TL N} $ \ Infty $ n = 1 Markov Trace的限制是偶然的。
Let R f = Z[A $\pm$1 ] be the algebra of Laurent polynomials in the variable A and let R a = Z[A $\pm$1 , z 1 , z 2 ,. .. ] be the algebra of Laurent polynomials in the variable A and standard polynomials in the variables z 1 , z 2 ,. .. . For n $\ge$ 1 we denote by VB n the virtual braid group on n strands. We define two towers of algebras {VTL n (R f)} $\infty$ n=1 and {ATL n (R a)} $\infty$ n=1 in terms of diagrams. For each n $\ge$ 1 we determine presentations for both, VTL n (R f) and ATL n (R a). We determine sequences of homomorphisms {$ρ$ f n : R f [VB n ] $\rightarrow$ VTL n (R f)} $\infty$ n=1 and {$ρ$ a n : R a [VB n ] $\rightarrow$ ATL n (R a)} $\infty$ n=1 , we determine Markov traces {T f n : VTL n (R f) $\rightarrow$ R f } $\infty$ n=1 and {T a n : ATL n (R a) $\rightarrow$ R a } $\infty$ n=1 , and we show that the invariants for virtual links obtained from these Markov traces are the f-polynomial for the first trace and the arrow polynomial for the second trace. We show that, for each n $\ge$ 1, the standard Temperley-Lieb algebra TL n embeds into both, VTL n (R f) and ATL n (R a), and that the restrictions to {TL n } $\infty$ n=1 of the two Markov traces coincide.
