The double of representations of Cohomological Hall Algebra for   $A_1$-quiver
  We compute two representations of COHA for $A_1$-quiver. The two untwisted representations can be combined into a representation of $D_{n+1}$ Lie algebra. The untwisted increasing representation and the twisted decreasing representation can be combined into a representation of a finite Clifford algebra. 
Xinli Xiao
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