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Are there naturally-arising Lie algebras over $\mathbf{C}(t)$? I have such an algebra, and I want to compute its cohomology–but I'm out of ideas. Are there known methods or theory for dealing with this problem?

My Lie algebra is generated by $u_i,v_i$ $i\in\mathbb{N}$. The bracket is as follows: $[u_i,u_j]=(i−j)u_{i+j}, [u_i,v_j]=(t+i−j)v_{i+j},[v_i,v_j]=0$.

It arose as a tool for computing stable Betty numbers of $L_1/L_n$.

Are there naturally-arising Lie algebras(or superalgebras) over $\mathbf{C}(t)$? I have such an algebra, and I want to compute its cohomology–but I'm out of ideas. Are there known methods or theory for dealing with this problem?

My Lie superalgebra is generated by $u_i $ and $ v_i,$ $i\in\mathbb{N},$ $|u_i|=1,|v_i|=0$. The bracket is as follows: $[u_i,u_j]=(i−j)u_{i+j}, [u_i,v_j]=-(t+i−j)v_{i+j},[v_i,v_j]=0$.

It arose as a tool for computing stable Betty numbers of $L_1/L_n$.

Are there naturally-arising Lie algebras over $\mathbf{C}(t)$? I have such an algebra, and I want to compute its cohomology–but I'm out of ideas. Are there known methods or theory for dealing with this problem?

Are there naturally-arising Lie algebras over $\mathbf{C}(t)$? I have such an algebra, and I want to compute its cohomology–but I'm out of ideas. Are there known methods or theory for dealing with this problem?

My Lie algebra is generated by $u_i,v_i$ $i\in\mathbb{N}$. The bracket is as follows: $[u_i,u_j]=(i−j)u_{i+j}, [u_i,v_j]=(t+i−j)v_{i+j},[v_i,v_j]=0$.

It arose as a tool for computing stable Betty numbers of $L_1/L_n$.

Are there any naturally arising Lie algebras over $\mathbb{C}(t)$? I have such algebra myself and I need to compute its cohomology, but I'm out of ideas. Maybe there are some special methods or some kind of theory for this problem?

Are there naturally-arising Lie algebras over $\mathbf{C}(t)$? I have such an algebra, and I want to compute its cohomology–but I'm out of ideas. Are there known methods or theory for dealing with this problem?