| Summary: | Koam and Pirashivili developed the equivariant version of Hochschild cohomology by mixing the standard chain complexes computing group with associative algebra cohomologies to obtain the bicomplex <inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>C</mi> <mo stretchy="false">˜</mo> </mover> <msubsup> <mrow></mrow> <mi>G</mi> <mo>*</mo> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. In this paper, we form a new bicomplex <inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi>F</mi> <mo stretchy="false">˘</mo> </mover> <msubsup> <mrow></mrow> <mi>G</mi> <mo>*</mo> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> by deleting the first column and the first row and reindexing. We show that <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mover accent="true"> <mi mathvariant="script">H</mi> <mo stretchy="false">˘</mo> </mover> <mi>G</mi> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> classifies the singular extensions of oriented algebras.
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